BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pavlos Motakis (UIUC) DTSTART:20200410T140000Z DTEND:20200410T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/1 DESCRIPTION:Title: Coarse Universality\nby Pavlos Motakis (UIUC) as part of Banach spaces webinars\n\n\nAbstract\nThe Bourgain index is a tool that c an be used to show that if a separable Banach space contains isomorphic co pies of all members of a class $C$ then it must contain isomorphic copies of all separable Banach spaces. This can be applied\, e.g.\, to the class $C$ of separable reflexive spaces. Notably\, the embedding of each member of $C$ does not witness the universality of $X$. We investigate a natural coarse analogue of this index which can be used\, e.g.\, to show that a se parable metric space that contains coarse copies of all members in certain “small" classes of metric spaces $C$ then $X$ contains a coarse copy of $c_0$ and thus of all separable metric spaces.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Ostrovskii (St. John's) DTSTART:20200417T140000Z DTEND:20200417T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/2 DESCRIPTION:Title: Transportation cost spaces\, also known as Arens-Eells space s\, Lipschitz-free spaces\, Wasserstein 1 spaces\, etc.\nby Mikhail Os trovskii (St. John's) as part of Banach spaces webinars\n\n\nAbstract\nAft er a brief introduction I shall talk about $\\ell_1$-subspaces in transpor tation cost spaces. Results presented in this talk\, mentioned in it\, or related to it\, can be found in joint papers with Stephen Dilworth\, Seych elle Khan\, Denka Kutzarova\, Mutasim Mim\, and Sofiya Ostrovska\, see \n< br>\n\nLipschitz free spaces on finite metric spaces\n
\n\nGeneralized transportation cost spaces\n
\n\nIsometric copies of $\\ell^n_{\\infty}$ and $\\el l_1^n$ in transportation cost spaces on finite metric spaces\n
\n\n On relations between transporta tion cost spaces and $L_1$\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomasz Kania (Czech Academy of Sciences) DTSTART:20200424T140000Z DTEND:20200424T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/3 DESCRIPTION:Title: Quantifying Kottman's constant\nby Tomasz Kania (Czech A cademy of Sciences) as part of Banach spaces webinars\n\n\nAbstract\nKottm an's constant\, $K(X)$\, of a Banach space $X$ is the supremum over those $d>0$ for which the unit sphere of $X$ contains a $d$-separated sequence. It is known that $K(X)>1$ for every infinite-dimensional space $X$ (the El ton–Odell theorem). I will present certain estimates related to interpol ation spaces\, twisted sums\, and other classes of Banach spaces $X$ conce rning the isomorphic Kottman constant\, defined as the infimum of $K(Y)$\, where $Y$ ranges over all renormings of $X$. \nI will also comment on oth er related constants (such as the disjoint one defined for Banach lattices ) and their symmetric analogs.\n\n\n\nThis talk is based on papers with J. M. F. Castillo\, M\, González\, P. L. Papini (PAMS 2020+) and P. Hájek\ , T. Russo (JFA 2018).\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Freeman (St Louis University) DTSTART:20200501T140000Z DTEND:20200501T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/4 DESCRIPTION:Title: A Schauder basis for $L_2$ consisting of non-negative fun ctions\nby Daniel Freeman (St Louis University) as part of Banach spac es webinars\n\n\nAbstract\nWe will discuss what coordinate systems can be created for $L_p(\\R)$ using only non-negative functions with $1 \\leq p<\ \infty$. In particular\, we will describe the construction of a Schauder b asis for $L_2(\\mathbb R)$ consisting of only non-negative functions. We w ill conclude with a discussion of some related open problems. \n\nThis is joint work with Alex Powell and Mitchell Taylor.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Gartland (UIUC) DTSTART:20200508T140000Z DTEND:20200508T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/5 DESCRIPTION:Title: Lipschitz free spaces over locally compact metric spaces \nby Chris Gartland (UIUC) as part of Banach spaces webinars\n\n\nAbstract \nThe talk is generally about questions of local-to-global phenomena in me tric and Banach space theory. There are two motivating questions: Let X be a complete\, locally compact metric space. (1) If every compact subset of X biLipschitz embeds into a Banach space with the Radon-Nikodym property\ , is the same true of X? (2) If the Lipschitz free space over K has the Ra don-Nikodym property for every compact subset K of X\, is the same true fo r the Lipschitz free space over X? We will first overview the theory of no n-biLipschitz embeddability of metric spaces into Banach spaces with the R adon-Nikodym property\, and then discuss an idea developed in an attempt t o answer (2). We will show how this idea may be used to answer modified ve rsions of (2) when the Radon-Nikodym property is replaced by the Schur or approximation property.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Gideon Schechtman (Weizmann Institute of Science) DTSTART:20200515T140000Z DTEND:20200515T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/6 DESCRIPTION:Title: The number of closed ideals in $L(L_p)$\nby Gideon Schec htman (Weizmann Institute of Science) as part of Banach spaces webinars\n\ n\nAbstract\nI intend to review what is known about the closed ideals in t he Banach algebras $L(L_p(0\,1))$. Then concentrate on a recent result of Bill Johnson and myself s howing that for $1\\lt p\\not= 2\\lt \\infty$ there are exactly $2^{2^{\\a leph_0}}$ different closed ideals in $L(L_p(0\,1))$.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Miguel Martin (University of Granada) DTSTART:20200529T140000Z DTEND:20200529T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/7 DESCRIPTION:Title: On Quasi norm attaining operators between Banach spaces\ nby Miguel Martin (University of Granada) as part of Banach spaces webinar s\n\n\nAbstract\nThis talk deals with a very recently introduced weakened notion of norm attainment for bounded linear operators. An operator $T\\co lon X \\longrightarrow Y$ between the Banach spaces $X$ and $Y$ is quas i norm attaining if there is a sequence $(x_n)$ of norm one elements i n $X$ such that $(Tx_n)$ converges to some $u\\in Y$ with $\\|u\\|=\\|T\\| $. Norm attaining operators in the usual sense (i.e. operators for which t here is a point in the unit ball where the norm of its image equals the no rm of the operator) and compact operators satisfy this definition. The mai n result is that strong Radon-Nikodým operators (such as weakly compact o perators can be approximated by quasi norm attaining operators (even by a stronger version of the definition)\, a result which does not hold for nor m attaining operators. This allows us to give characterizations of the Rad on-Nikodým property in term of the denseness of quasi norm attaining oper ators for both domain spaces and range spaces\, extending previous results by Bourgain and Huff. We will also present positive and negative results on the denseness of quasi norm attaining operators\, characterize both fin ite dimensionality and reflexivity in terms of quasi norm attaining operat ors\, discuss conditions to obtain that quasi norm attaining operators are actually norm attaining\, study the relationship with the norm attainment of the adjoint operator. We will finish the talk discussing some remarks and open questions.\n\nThe content of the talk is based on the recent prep rint On Quasi norm attaining op erators between Banach spaces by Geunsu Choi\, Yun Sung Choi\, Mingu Jung\ , and Miguel Martin.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Braga (University of Virginia) DTSTART:20200626T140000Z DTEND:20200626T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/8 DESCRIPTION:by Bruno Braga (University of Virginia) as part of Banach spac es webinars\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Tradacete (Instituto de Ciencias Matemáticas) DTSTART:20200522T140000Z DTEND:20200522T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/9 DESCRIPTION:Title: Free Banach lattices\nby Pedro Tradacete (Instituto de C iencias Matemáticas) as part of Banach spaces webinars\n\n\nAbstract\nWe will start recalling the construction of the free Banach lattice \ngenera ted by a Banach space. This notion provides a new link betweeen \nBanach space and Banach lattice properties. We will show how this can \nbe usefu l to tackle some problems and discuss some open questions. The \nmaterial of the talk is partially based on the following papers:\n\nThe free Banach lattice generated by a Banach space by Antonio Avilés\, José Rodríguez\, Pedro Tradacete\, J. Funct. Anal. 274 (2018)\, no. 10\, 2955-2977\n\nThe free Banach lattices generated by $\\ell_p$ and $c_0$ by Antonio Avilés\, Pedro Tradacete\, Ignacio Villanueva\, Rev.Mat. Compl utense 32 (2019)\, no. 2\, 353-364.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Denny Leung (National University of Singapore) DTSTART:20200605T140000Z DTEND:20200605T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/10 DESCRIPTION:Title: Local convexity in $L^0$\nby Denny Leung (National Univ ersity of Singapore) as part of Banach spaces webinars\n\n\nAbstract\nLet $(\\Omega\,\\Sigma\,\\mathbb P)$ be a nonatomic probability space and let $L^0(\\Omega\,\\Sigma\,\\mathbb P)$ be the space of all measurable functio ns on $(\\Omega\,\\Sigma\,\\mathbb P)$.\nWe present some results character izing the convex sets in $L^0$ that are locally convex with respect to the topology of convergence in measure. The work is motivated by results of Kardaras & Zitkovic (PAMS 2013) and Kardaras (JFA 2014) and is relevant to mathematical economics/finance.\n\nThe talk is based on joint work with N iushan Gao and Foivos Xanthos:\n\nA local Hahn-Banach Theorem and its applications\, Arch. Math.\, 112(20 19)\, 521-529. \n\n On loca l convexity in $L^0$ and switching probability measures. \n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Noé de Rancourt (Kurt Gödel Research Center) DTSTART:20200612T140000Z DTEND:20200612T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/11 DESCRIPTION:Title: Local Banach-space dichotomies\nby Noé de Rancourt (Ku rt Gödel Research Center) as part of Banach spaces webinars\n\n\nAbstract \nI will present some results of a recent joint preprint with Wilson Cuell ar Carrera and Valentin Ferenczi. These results are generalizations of Ban ach-space dichotomies due to\nGowers and to Ferenczi–Rosendal\; the orig inal dichotomies aimed at building a classification of separable Banach sp aces "up to subspaces". Our generalizations are "local versions" of the or iginal dichotomies\, that is\, we ensure that the outcome space can be tak en in a prescribed family of subspaces. One of the most interesting exampl es of such a family is the family of all non-Hilbertian Banach spaces\; he nce\, our results are a first step towards a classification of non-Hilbert ian\, $\\ell_2$-saturated Banach spaces\, up to subspaces. If time permits \, I will present some applications of our work to a conjecture by Ferencz i and Rosendal about the number of subspaces of a separable Banach space.\ n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Rosendal (UIC and NSF) DTSTART:20200619T140000Z DTEND:20200619T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/12 DESCRIPTION:Title: Two applications of Arens-Eells spaces to geometric group t heory and abstract harmonic analysis\nby Christian Rosendal (UIC and N SF) as part of Banach spaces webinars\n\n\nAbstract\nArens-Eells spaces (a ka Lipschitz free spaces or transportation cost spaces) give rise to inter esting examples of Banach spaces and provide analytic techniques within Ba nach space geometry\, but are also of importance as a tool for analysing o bjects outside Banach space theory using functional analytical techniques. I will present two such uses. The first is to abstract harmonic analysis where Arens-Eells spaces can be used to provide a very simple conceptual p roof of a recent characterisation of amenability of topological groups due to F. M. Schneider and A. Thom. The second application is to the geometri c study of topological groups\, namely\, to establish the Gromov correspon dence between coarse equivalence and topological couplings in the widest p ossible setting. Time permitting\, we also discuss some application of the harmonic analytical tools to the non-linear geometry of Banach spaces.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Gilles Lancien (Besançon) DTSTART:20200703T140000Z DTEND:20200703T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/13 DESCRIPTION:Title: Kalton's interlacing graphs and embeddings into dual Banach spaces\nby Gilles Lancien (Besançon) as part of Banach spaces webina rs\n\n\nAbstract\nA fundamental theorem of Aharoni (1974) states that ever y separable metric spaces bi-Lipschitz embeds into $c_0$. It is a major op en question to know whether any Banach space containing a Lipschitz copy o f $c_0$ must contain a subspace linearly isomorphic to $c_0$. In this talk \, we will consider similar questions in relation with the weaker notion o f coarse embeddings.\n \nIn a paper published in 2007\, a major step was t aken by Nigel Kalton\, who showed that a Banach space containing a coarse copy of $c_0$ cannot have all its iterated duals separable (in particular it cannot be reflexive). However\, it is still unknown whether such a spac e can be a separable dual. In this talk\, we will discuss some aspects of this question. Kalton's argument is based on the use of a special family o f metric graphs that we call ``Kalton's interlacing graphs''. We will give results about dual spaces containing equi-Lipschitz or equi-coarse copies of these graphs\, in relation with the Szlenk index\, and show their opti mality.\n\n\nThis is a joint work with B. de Mendonça Braga\, C. Petitjea n and A. Procházka.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Niels Laustsen (Lancaster University) DTSTART:20200710T140000Z DTEND:20200710T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/14 DESCRIPTION:Title: A $C(K)$-space with few operators and few decompositions\nby Niels Laustsen (Lancaster University) as part of Banach spaces webin ars\n\n\nAbstract\nI shall report on joint work with Piotr Koszmider (IMPAN) concerning the closed su bspace of $\\ell_\\infty$ generated by $c_0$ and the characteristic functi ons of elements of an uncountable\, almost disjoint family $A$ of infinite subsets of the natural numbers. This Banach space has the form $C_0(K_A)$ for a locally compact Hausdorff space $K_A$ that is known under many name s\, including $\\Psi$-space and Isbell--Mrówka space.\n\nWe construct an uncountable\, almost disjoint family $A$ such that the algebra of all boun ded linear operators on $C_0(K_A)$ is as small as possible in the precise sense that every bounded linear operator on $C_0(K_A)$ is the sum of a sca lar multiple of the identity and an operator that factors through $c_0$ (w hich in this case is equivalent to having separable range). This implies t hat $C_0(K_A)$ has the fewest possible decompositions: whenever $C_0(K_A)$ is written as the direct sum of two infinite-dimensional Banach spaces $X $ and $Y$\, either $X$ is isomorphic to $C_0(K_A)$ and $Y$ to $c_0$\, or v ice versa. These results improve\nprevious work of Koszmider in which an e xtra set-theoretic hypothesis was required.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Javier Alejandro Chávez-Domínguez (University of Oklahoma) DTSTART:20200717T140000Z DTEND:20200717T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/15 DESCRIPTION:Title: Completely coarse maps are real-linear\nby Javier Aleja ndro Chávez-Domínguez (University of Oklahoma) as part of Banach spaces webinars\n\n\nAbstract\nIn this talk I will present joint work with Bruno M. Braga\, continuing the study of the nonlinear geometry of operator spac es that was recently started by Braga and Sinclair.\n\nOperator spaces are Banach spaces with an extra “noncommutative” structure. Their theory sometimes resembles very closely the Banach space case\, but other times i s very different. Our main result is an instance of the latter: a complete ly coarse map between operator spaces (that is\, a map such that the seque nce of its amplifications is equi-coarse) has to be real-linear.\n\nContin uing the search for an “appropriate” framework for a theory of the non linear geometry of operator spaces\, we introduce a weaker notion of embed dability between them and show that it is strong enough for some applicati ons. For instance\, we show that if an infinite dimensional operator space $X$ embeds in this weaker sense into Pisier's operator Hilbert space OH\, then $X$ must be completely isomorphic to OH.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Florent Baudier (TAMU) DTSTART:20200724T140000Z DTEND:20200724T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/16 DESCRIPTION:Title: $L_1$-embeddability of lamplighter metrics\nby Florent Baudier (TAMU) as part of Banach spaces webinars\n\n\nAbstract\nLamplighte r groups are important and well-studied objects in (geometric) group theor y as they provide examples of groups with a variety of interesting geometr ic/algebraic properties. The lamplighter construction can naturally be ext ended to apply to graphs and is instrumental in the study of random walks on graphs. \nHowever\, much remains to be understood regarding the embedda bility of lamplighters groups or graphs into classical Banach spaces.\nIns pired by works on the earthmover distance I will explain how the machinery of stochastic embeddings into tree metrics can be fruitfully applied to t he study of $L_1$-embeddability of lamplighter metrics and how it provides general upper bounds on the $L_1$-distortion of finite lamplighter graphs (and groups). I will then discuss an application to the coarse embeddabil ity of the planar lamplighter group and if time permits an application to linear embeddings of Arens-Eells spaces over finite metric spaces into fin ite-dimensional $\\ell_1$-spaces. The talk will be targeted towards non-sp ecialists.\n\nBased on joint works with P. Motakis (UIUC)\, Th. Schlumprec ht (Texas A&M)\, and A. Zsák (Peterhouse\, Cambridge)\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Ferenczi (University of São Paulo) DTSTART:20200731T140000Z DTEND:20200731T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/17 DESCRIPTION:Title: On envelopes and $L_p$ spaces\nby Valentin Ferenczi (Un iversity of São Paulo) as part of Banach spaces webinars\n\n\nAbstract\nT his talk is based on a work in progress with Jordi Lopez-Abad. \n\n\nWe de fine\, inside a given space $X$\, the envelope ${\\rm Env}(Y)$ of \na subs pace $Y$ as the largest subspace such that\, for any net of surjective iso metries on $X$\, pointwise convergence to the identity on $Y$ implies poi ntwise convergence to the identity on ${\\rm Env}(Y)$. This is reminiscent of the study of Korovkin sets in spaces $C(K)$ or $L_p(\\mu)$ (initiated by P.P. Korovkin in 1960).\n\nWe shall mention some results of a\nrecent paper of J. Lopez-Abad\, B. Mbombo\, and S. Todorcevic and myself (2019): different notions of ultrahomogeneity of Banach spaces will be stated (AUH \, Fraïssé) which are relevant to multidimensional versions of Mazur rot ations problem. Known examples of these are the Gurarij space and the spac es $L_p$'s for $p \\neq 4\,6\,8\,\\ldots$. We shall address the conjecture that these are the only separable examples.\n\n The notion of envelope is especially relevant to the study of AUH or Fraïssé spaces. \nIn particu lar we shall compute explicitly certain envelopes in $L_p$-spaces and conc lude by giving a meaning to potentially new objects such as $L_p/\\ell_2$ \, $L_p/L_q$\, $L_p/\\ell_q$\, for appropriate values of $p$ and $q$.\n\n\ nPartially supported by Fapesp\, 2016/25574-8 and CNPq\, 303731/2019-2.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Beanland (Washington and Lee) DTSTART:20200403T140000Z DTEND:20200403T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/18 DESCRIPTION:Title: Closed ideals of operators on the Tsirelson and Schreier sp aces\nby Kevin Beanland (Washington and Lee) as part of Banach spaces webinars\n\n\nAbstract\nSignificant progress has been made in our understa nding of\nthe lattice of closed ideals of the Banach algebra $\\mathcal{B} (X)$ of\nbounded operators on a Banach space $X$ over the last decade. I s hall\nsurvey some highlights of this development and then focus on the\nou tcomes of an ongoing collaboration with Niels Laustsen (Lancaster Universi ty\, UK) \nand Tomasz Kania (Czech Academy of Sciences) in\nwhich we study the closed ideals of $\\mathcal{B}(X)$ in the case\nwhere $X$ is either Tsirelson's Banach space or a Schreier space\nof finite order.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Pete Casazza (University of Missouri) DTSTART:20200807T140000Z DTEND:20200807T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/19 DESCRIPTION:Title: Tsirelson space\, explicitly definable Banach space\, impli citly definable Banach space\nby Pete Casazza (University of Missouri) as part of Banach spaces webinars\n\n\nAbstract\nWe prove that Tsirelson' s space cannot be defined explicitly from the classical Banach sequence sp aces.\nWe also prove that any Banach space that is explicitly definable fr om a class of spaces that contain $\\ell_p$ or $c_0$ must contain $\\ell_p $ or $c_0$ as well.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Young (NYU) DTSTART:20200814T140000Z DTEND:20200814T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/20 DESCRIPTION:Title: Metric differentiation and Lipschitz embeddings in $L_p$ sp aces\nby Robert Young (NYU) as part of Banach spaces webinars\n\n\nAbs tract\nKadec and Pełczyński showed that if $1\\le p\\lt 2\\lt q\\lt \\in fty$ and $X$ is a Banach space that embeds into both $L_p$ and $L_q$\, the n $X$ is isomorphic to a Hilbert space. The search for metric analogues of such a result is intertwined with the Ribe program and metric theories of type and cotype. Recently\, with Assaf Naor\, we have constructed a metri c space based on the Heisenberg group which embeds into $L_1$ and $L_4$ bu t not in $L_2$. In this talk\, we will describe this example\, explain why embeddings of the Heisenberg group into Banach spaces must be "bumpy" at many scales\, and discuss how to bound the bumpiness of Lipschitz maps to Banach spaces.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Khazhakanush Navoyan (Thompson Rivers University) DTSTART:20200821T140000Z DTEND:20200821T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/21 DESCRIPTION:Title: The positive Schur property on spaces of regular multilinea r operators\nby Khazhakanush Navoyan (Thompson Rivers University) as p art of Banach spaces webinars\n\n\nAbstract\nIn this paper we give necessa ry and sufficient conditions for the space of regular multilinear operator s from the product of Banach lattices to a Dedekind complete Banach lattic e to have the positive Schur property. We also characterize the positive S chur property on the positive projective mm-fold tensor product of Banach lattices\, $m\\in\\mathbb{N}$\, and on its dual. This is a joint work with Geraldo Botelho\, Qingying Bu and Donghai Ji.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Mary Angelica Gramcko-Tursi (UIUC) DTSTART:20200904T140000Z DTEND:20200904T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/22 DESCRIPTION:Title: A separable universal homogeneous Banach lattice\nby Ma ry Angelica Gramcko-Tursi (UIUC) as part of Banach spaces webinars\n\n\nAb stract\nWe prove the existence of a separable approximately ultra-homogene ous Banach lattice BL that is isometrically universal for separable Banach lattices. This is done by showing that the class of Banach lattices has t he Amalgamation Property\, and thus finitely generated Banach lattices for m a metric Fraïssé class. Some additional results about the structural p roperties of BL are also proven.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Bence Horváth (Institute of Mathematics of the Czech Academy of S ciences) DTSTART:20200911T140000Z DTEND:20200911T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/23 DESCRIPTION:Title: When are surjective algebra homomorphisms of $\\mathcal{B}( X)$ automatically injective?\nby Bence Horváth (Institute of Mathemat ics of the Czech Academy of Sciences) as part of Banach spaces webinars\n\ n\nAbstract\nA classical result of Eidelheit asserts that if $X$ and $Y$ a re Banach\nspaces then they are isomorphic if and only if their algebras o f\noperators $\\mathcal{B}(X)$ and $\\mathcal{B}(Y)$ are isomorphic as Ban ach\nalgebras\, in the sense that there is a continuous bijective algebra\ nhomomorphism $\\psi: \\\, \\mathcal{B}(X) \\rightarrow \\mathcal{B}(Y)$. It is\nnatural to ask whether for some class of Banach spaces $X$ this the orem\ncan be strengthened in the following sense: If $Y$ is a non-zero Ban ach\nspace and $\\psi: \\mathcal{B}(X) \\rightarrow \\mathcal{B}(Y)$ is a\ nsurjective algebra homomorphism\, is $\\psi$ automatically injective?\n\n It is easy to see that for a ``very nice'' class Banach spaces\, such as\n $c_0$ and $\\ell_p$\, where $1 \\leq p < \\infty$\, the answer is positive .\nFurther examples include $\\ell_{\\infty}$ and $( \\oplus_{n=1}^{\\inft y}\n\\ell_2^n )_{c_0}$ and its dual space $\\left( \\oplus_{n=1}^{\\infty} \n\\ell_2^n \\right)_{\\ell_1}$\, and the arbitrarily distortable Banach s pace\n$\\mathbf{S}$ constructed by Schlumprecht. In recent joint work with \nTomasz Kania it was shown that ``long'' sequence spaces of the form\n$c_ 0(\\lambda)$\, $\\ell_{\\infty}^c(\\lambda)$ and $\\ell_p(\\lambda)$ (wher e\n$1 \\leq p < \\infty$) also enjoy this property.\n\nIn the other direct ion\, with the aid of a result of\nKania--Koszmider--Laustsen we will show that for any separable\,\nreflexive Banach space $X$ there is a Banach sp ace $Y_X$ and a\nsurjective algebra homomorphism $ \\psi: \\\, \\mathcal{B }(Y_X) \\rightarrow\n\\mathcal{B}(X)$ which is not injective.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Tommaso Russo (Czech Technical University in Prague) DTSTART:20200828T140000Z DTEND:20200828T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/24 DESCRIPTION:Title: Asplund Banach spaces with norming Markuševič bases\ nby Tommaso Russo (Czech Technical University in Prague) as part of Banach spaces webinars\n\n\nAbstract\nThe first existence result for norming Mar kuševič bases (M-bases\, for short) in Banach spaces is perhaps due to M arkuševič\, who proved that every separable Banach space admits a 1-norm ing M-basis. After the introduction of projectional resolutions of the ide ntity\, it became clear that such bases also exist in every reflexive Bana ch space.\n\nIn order to understand the strength of the said notion\, a na tural problem at the time was then to characterise those (non-separable) B anach spaces that admit a norming M-basis. Perhaps the main question\, due originally to John and Zizler and that was solved very recently by P. Há jek\, was whether every weakly compactly generated (WCG) Banach space admi ts a norming M-basis.\n\nIn the converse direction\, it was asked by Gille s Godefroy if an Asplund space with a norming M-basis is necessarily WCG. In the talk\, based on a joint work with P. Hájek\, J. Somaglia\, and S. Todorčević\, we shall discuss our recent negative answer to the latter q uestion. Moreover\, the construction yields an interesting example of a sc attered compact space that also solves a question due to Wiesław Kubiś a nd Arkady Leiderman.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Phillips (University of Oregon) DTSTART:20200918T140000Z DTEND:20200918T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/25 DESCRIPTION:Title: Operator algebras on $L_p$ spaces\nby Chris Phillips (U niversity of Oregon) as part of Banach spaces webinars\n\n\nAbstract\nSurp risingly\, there appears to be a rich theory of "C* like"\noperator algebr as on $L_p$ spaces. It is far from actual C*-algebras\,\nbut analogs of so me of the basic examples of C*-algebras have\nanalogs on $L_p$ spaces whic h share at least some of the properties\nof the C* examples. Some of the m ethods of proof are very different.\n\nThere are many open problems. We do not even have a definition of\nwhat it means for an $L_p$ operator algebr a to be "C* like"--just\nsome heuristic criteria.\n\nThis talk will try to give an impression of the current state of\nthe theory\, focussing on sev eral classes of examples. It will not\nassume significant knowledge of C*- algebras.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Paata Ivanisvili (North Carolina State) DTSTART:20200925T140000Z DTEND:20200925T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/26 DESCRIPTION:Title: Sharpening the triangle inequality in $L_p$ spaces\nby Paata Ivanisvili (North Carolina State) as part of Banach spaces webinars\ n\n\nAbstract\nThe classical triangle inequality in $L_p$ estimates the n orm of the sum of two functions in terms of the sums of the norms of these functions. \nPerhaps one drawback of this estimate is that it does not se e how "orthogonal" these functions are. \nFor example\, if $f$ and $g$ a re not identically zero and they have disjoint supports then the triangle inequality is pretty strict (say for $p>1$). \nMotivated by the $L_2$ case \, where one has a trivial inequality $||f+g||^2 \\leq ||f||^2 + ||g||^2 + 2 |fg|_1$\, one can think about the quantity $|fg|_1$ as measuring the "overlap" between $f$ and $g$. \nWhat is the correct analog of this est imate in $L_p$ for $p$ different than 2? My talk will be based on a joint work with Carlen\, Frank and Lieb where we obtain one extension of this e stimate in $L_p$\, thereby proving and improving the suggested possible es timates by Carbery\, and another work with Mooney where we further refine these estimates. The estimates will be provided for all real $p$'s.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Pelczar-Barwacz (Jagiellonian University) DTSTART:20201002T140000Z DTEND:20201002T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/27 DESCRIPTION:Title: Small operator ideals on the Schlumprecht and Schreier spac es\nby Anna Pelczar-Barwacz (Jagiellonian University) as part of Banac h spaces webinars\n\n\nAbstract\nI report on the joint work with Antonis M anoussakis\, showing that there are $2^{2^{\\aleph_0}}$ many different clo sed operator ideals on the Schlumprecht space and every Schreier space of finite order admits a chain of the cardinality $2^{\\aleph_0}$ of closed o perator ideals.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Temlyakov (University of South Carolina) DTSTART:20201009T140000Z DTEND:20201009T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/28 DESCRIPTION:Title: Sampling discretization of integral norms\nby Vladimir Temlyakov (University of South Carolina) as part of Banach spaces webinars \n\n\nAbstract\nThe talk is devoted to discretization of integral norms of functions from\na given finite dimensional subspace. Even though this pro blem is extremely important in applications\, its systematic study has beg un recently.\nIn this talk we discuss a conditional theorem for all integr al norms $L_q$\, $1\\le q<\\infty$.\nA new technique\, which works well f or discretization of the integral norms\, was used. It is\na combination o f probabilistic technique with results on the entropy numbers in the unifo rm norm.\nWe discuss the behavior of the entropy numbers of classes of fun ctions with bounded integral norms from a given finite dimensional linear subspace. \nUpper bounds of these entropy numbers in the uniform norm are obtained and applied \nto establish a Marcinkiewicz type discreti zation theorem for integral norms of functions from a given finite d imensional subspace. \nAs an application of the general con ditional theorem\, we discuss a new Marcinkiewicz type\ndiscretization for the multivariate trigonometric polynomials with frequencies from the hyp erbolic crosses.\nIt is shown that recently developed techniques allow us to improve the known results in this direction.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Mitchell Taylor (UC Berkeley) DTSTART:20201016T140000Z DTEND:20201016T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/29 DESCRIPTION:Title: Free Banach lattices: subspace structure and basic sequence s\nby Mitchell Taylor (UC Berkeley) as part of Banach spaces webinars\ n\n\nAbstract\nGiven a Banach space E\, one can associate a Banach lattice FBL[E] with the property that every bounded operator from E to a Banach l attice X extends uniquely to a lattice homomorphism from FBL[E] into X. We will discuss the structure of FBL[E]\, and give complete answers to quest ions like when does an embedding of E into F induce a lattice embedding of FBL[E] into FBL[F]? This is joint work with Timur Oikhberg\, Pedro Tradac ete and Vladimir Troitsky.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Przemysław Wojtaszczyk (Polish Academy of Sciences) DTSTART:20201023T140000Z DTEND:20201023T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/30 DESCRIPTION:Title: Quasi-greedy bases in $p$-Banach spaces\nby Przemysław Wojtaszczyk (Polish Academy of Sciences) as part of Banach spaces webinar s\n\n\nAbstract\nThis talk is based on the paper F. Albiac\, J.L. Ansorena and P.W. \nOn certain subspaces of $\\ell_p$ for $0\\lt p\\le 1$ and \nth eir applications to conditional quasi-greedy bases in $p$-Banach spaces\, Mathematische Annalen--available on line.\n \nWe construct new quasi-gree dy bases in $\\ell_p$ and in the \nkernels of certain quotient maps from $ \\ell_p $ onto $L_p$\,\n$0\\lt p\\leq 1$ and study its properties. We not e that all the kernels we study are isomorphic\; we denote this space as ${\\mathfrak l}_p$. \nWe show that there is continuum of non-equivalent q uasi-greedy\nbases in $\\ell_p$ and ${\\mathfrak l }_p$ and we study the \n conditionality of those bases.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Reis (University of Washington) DTSTART:20201030T140000Z DTEND:20201030T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/31 DESCRIPTION:Title: An Elementary Exposition of Pisier's Inequality\nby Vic tor Reis (University of Washington) as part of Banach spaces webinars\n\n\ nAbstract\nPisier's inequality is central in the study of normed spaces an d has important applications in geometry. We provide an elementary proof o f this inequality by constructing an explicit linear proxy function for a suitable probability distribution\, thus avoiding some non-constructive st eps in previous proofs. We also show a simplification of Bourgain's constr uction which is sufficient to give a nearly tight matching lower bound.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Dirk Werner (Freie Universität Berlin) DTSTART:20201106T150000Z DTEND:20201106T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/32 DESCRIPTION:Title: Vector space structure in the set of norm attaining functio nals\nby Dirk Werner (Freie Universität Berlin) as part of Banach spa ces webinars\n\n\nAbstract\nThe talk discusses the existence (or non-exist ence) of vector subspaces of\nthe dual space consisting entirely of norm a ttaining functionals.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Eva Pernecka (Czech Technical University in Prague) DTSTART:20201113T150000Z DTEND:20201113T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/33 DESCRIPTION:Title: Lipschitz free spaces and their biduals\nby Eva Perneck a (Czech Technical University in Prague) as part of Banach spaces webinars \n\n\nAbstract\nWe will study continuous linear functionals on Lipschitz s paces with special focus on those belonging to canonical preduals\, the Li pschitz free spaces. We will show that in order to verify weak$^*$ continu ity of a functional\, it suffices to do so for bounded monotone nets of Li pschitz functions. Then\, after introducing a notion of support for the fu nctionals\, we will discuss their relation to measures. In particular\, we will identify the functionals induced by measures as those functionals th at admit a Jordan-like decomposition into a positive and a negative part. The talk will be based on joint work with Ramón J. Aliaga.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Jamal Kawach (University of Toronto) DTSTART:20201120T150000Z DTEND:20201120T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/34 DESCRIPTION:Title: Approximate Ramsey properties of Fréchet spaces\nby Ja mal Kawach (University of Toronto) as part of Banach spaces webinars\n\n\n Abstract\nIn this talk we will consider various Fraïssé-theoretic aspect s of Fréchet spaces\, which we view as topological vector spaces equipped with a compatible sequence of semi-norms. We will show that certain class es of finite-dimensional Fréchet spaces satisfy a version of the approxim ate Ramsey property for Banach spaces. We will then see how this property is related to the topological dynamics of the isometry groups of approxima tely ultrahomogeneous Fréchet spaces. This talk contains joint work in pr ogress with Jordi López-Abad.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonis Manoussakis (Technical University of Crete) DTSTART:20201127T150000Z DTEND:20201127T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/35 DESCRIPTION:Title: A variant of the James tree space\nby Antonis Manoussa kis (Technical University of Crete) as part of Banach spaces webinars\n\n\ nAbstract\nWe will discuss the first part of a work in progress\, leading to the construction of an\n $\\ell_{2}$-saturated $d_{2}-$H.I. space. Th e class of\n $d_{2}$-H.I. Banach spaces is defined in a recent work of W .Cuellar\n Carrera\, N. de Rancourt and V. Ferenczi where also the proble m of\n the existence of $\\ell_{2}$-saturated $d_{2}$-H.I space was posed . In\n this talk we will present a classical analogue of this space\, wh ich\n is a reflexive space with an unconditional basis\, based on the Ja mes tree construction. We will discuss its properties and its connection to the desired $d_{2}$-H.I space.\n\nJoint work with Spiros Argyros and P avlos Motakis\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Schlumprecht (Texas A&M) DTSTART:20201204T150000Z DTEND:20201204T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/36 DESCRIPTION:by Thomas Schlumprecht (Texas A&M) as part of Banach spaces we binars\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Jose Luis Ansorena (Jose Luis Universidad de La Rioja) DTSTART:20201211T150000Z DTEND:20201211T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/37 DESCRIPTION:by Jose Luis Ansorena (Jose Luis Universidad de La Rioja) as p art of Banach spaces webinars\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Keith Ball (University of Warwick) DTSTART:20201215T163000Z DTEND:20201215T173000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/38 DESCRIPTION:Title: Restricted Invertibility\nby Keith Ball (University of Warwick) as part of Banach spaces webinars\n\n\nAbstract\nI will briefly d iscuss the Kadison-Singer problem and then explain a beautiful argument of Bourgain and Tzafriri that I will include in a forthcoming article in a v olume dedicated to Jean Bourgain.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Bill Johnson (Texas A&M) DTSTART:20210108T150000Z DTEND:20210108T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/39 DESCRIPTION:Title: Homomorphisms from $L(\\ell_p)$ and $L(L_p)$\nby Bill J ohnson (Texas A&M) as part of Banach spaces webinars\n\n\nAbstract\nThis i s joint work with N. C. Phillips and G.\nSchechtman.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Lechner (Johannes Kepler Universität Linz) DTSTART:20210115T150000Z DTEND:20210115T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/40 DESCRIPTION:Title: Restriced invertibility\, subsymmetric bases and factorizat ion\nby Richard Lechner (Johannes Kepler Universität Linz) as part of Banach spaces webinars\n\n\nAbstract\nGiven an unconditional normalized b asis $(e_j)_{j=1}^n$ of a Banach space $X_n$\, we consider\nconditions und er which an operator $T\\colon X_n\\to X_n$ with ``large diagonal'' can be inverted when\nrestricted to $X_\\sigma = [e_j : j\\in\\sigma]$ for a ``l arge'' set $\\sigma\\subset \\{1\,\\ldots\,n\\}$\n(restricted invertibilit y). We then discuss restricted invertibility and its close connection to\ nfinite dimensional quantitative factorization.\n\nIn the second part of t he talk\, we show that subsymmetric Schauder bases $(e_j)$ of an infinite\ ndimensional Banach space $X$ have the factorization property\, i.e.\\@ th e identity $I_X$ on $X$\nfactors through every bounded operator $T\\colon X\\to X$ with large diagonal. In Banach spaces with a\nSchauder basis\, th is type of result can often be proved using gliding-hump techniques\, but in\nnon-separable Banach spaces gliding-hump techniques seem unfeasible. However\, if $(e_j^*)$ is a\nnon-$\\ell^1$-splicing (there is no disjointl y supported $\\ell^1$-sequence in $X$) subsymmetric\nweak$^*$ Schauder bas is for the dual $X^*$ of $X$\, $(e_j^*)$ also has the factorization proper ty.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Ramon Aliaga (Universitat Politècnica de València) DTSTART:20210122T150000Z DTEND:20210122T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/41 DESCRIPTION:Title: The Radon-Nikodým and Schur properties in Lipschitz-free s paces\nby Ramon Aliaga (Universitat Politècnica de València) as part of Banach spaces webinars\n\n\nAbstract\nIn this talk I will sketch the p roof that\, for \nLipschitz-free spaces $\\mathcal{F}(M)$ over complete m etric spaces \n$M$\, several Banach space properties are equivalent inclu ding the \nRadon-Nikodým property\, the Schur property\, the Krein-Milma n property\, \nor not containing copies of $L_1$. These properties hold e xactly when \n$M$ is a purely 1-unrectifiable metric space. For compact $ M$\, these \nproperties are also equivalent to $\\mathcal{F}(M)$ being a dual Banach \nspace. The talk will be based on joint work with C. Gartlan d\, C. \nPetitjean and A. Procházka.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavlos Motakis (York University) DTSTART:20210129T150000Z DTEND:20210129T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/42 DESCRIPTION:Title: The space $L_1(L_p)$ is primary\nby Pavlos Motakis (Yor k University) as part of Banach spaces webinars\n\n\nAbstract\nWe show tha t $L_1(L_p)$\, the space of Bochner integrable functions with values in $L _p$\, $1\\lt p\\lt\\infty$\, is primary\, meaning that\, whenever we repr esent $L_1(L_p)$ as a complemented sum of two spaces one of them has to be isomorphic to $L_1(L_p)$. More generally\, the same result can be shown for $L_1(X)$\, where $X$ is closed linear span of the Haar system in a rearrangement invariant Banach space over $[0\,1)$\, except $L_\\infty$.\n \nThis is joint work with R. Lechner\, P.F.X Müller\, and Th. Schlumprech t.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Sophie Grivaux (Université de Lille) DTSTART:20210219T150000Z DTEND:20210219T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/43 DESCRIPTION:Title: Typical properties of contractions on $\\ell_p$-spaces\ nby Sophie Grivaux (Université de Lille) as part of Banach spaces webinar s\n\n\nAbstract\nGiven a separable Banach space $X$ of infinite dimension\ , one can consider\non the space $\\mathcal{B}(X)$ of bounded linear opera tors on $X$ several\nnatural topologies which turn the closed unit ball\n$ B_1(X)=\\{T\\in\\mathcal{B}(X)\;||T||\\le 1\\}$ into a Polish space\, i.e. a\nseparable and completely metrizable space.\n\nIn these talk\, I will p resent some results concerning typical properties\nin the Baire Category s ense of operators of $B_1(X)$ for these\ntopologies when $X$ is a $\\ell_p $-space\, our main interest being to\ndetermine whether typical contractio ns on these spaces have a non-trivial\ninvariant subspace or not.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Wallis (Elgin Community College) DTSTART:20210226T150000Z DTEND:20210226T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/44 DESCRIPTION:by Ben Wallis (Elgin Community College) as part of Banach spac es webinars\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio Avilés López (Universidad de Murcia) DTSTART:20210305T150000Z DTEND:20210305T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/45 DESCRIPTION:Title: Sequential octahedrality and L-orthogonal elements\nby Antonio Avilés López (Universidad de Murcia) as part of Banach spaces we binars\n\n\nAbstract\nGiven a Banach space $X$\, we consider the following two isometric properties\, variations on the notion of octahedrality that can be traced back to the work of B. Maurey:\n\n1. There is an element $ e^{**}$ in the sphere of the bidual such that $\\|e^{**}+x\\| = 1 + \\|x\\ |$ for every $x\\in X$.\n\n2. There is a sequence $(e_n)$ in the sphere of $X$ such that $\\lim_n \\|e_n+x\\| = 1 + \\|x\\|$\n\n\nUncountable sums p rovide examples that 1 does not imply 2. But the converse is unclear. It i s natural to conjecture that a weak$^*$-cluster point of the sequence $(e_ n)$ would give the desired $e^{**}$. This turns out to be independent of t he usual axioms of set theory. The proof involves understanding different kinds of ultrafilters that may or may not exist\, as well as a filter vers ion of the Lebesgue dominated convergence theorem\, similar to those consi dered by V. Kadets and A. Leonov. This is a joint work (in progress) with G. Mart\\'{\\i}nez Cervantes and A. Rueda Zoca.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Müller (Johannes Kepler Universität Linz) DTSTART:20210319T140000Z DTEND:20210319T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/46 DESCRIPTION:Title: Complex Convexity Estimates\, Extensions to $R ^n$\, and lo g-Sobolev Inequalities.\nby Paul Müller (Johannes Kepler Universität Linz) as part of Banach spaces webinars\n\n\nAbstract\nThe talk is based on joint work with P.Ivanishvili (North\nCarolina State University)\, A. Lindenberger (JKU) and M.\nSchmuckenschlaeger (JKU).\n\nWe extend complex uniform convexity estimates to $R^n$ and determine\nthe corresponding be st constants. Furthermore we provide the link to\nlog-Sobolev inequalities on the unit-sphere of $R^n$ and discuss several\nopen conjectures related to our work.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikael de la Salle (ENS Lyon) DTSTART:20210212T150000Z DTEND:20210212T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/47 DESCRIPTION:Title: On a duality between Banach spaces and operators\nby Mi kael de la Salle (ENS Lyon) as part of Banach spaces webinars\n\n\nAbstrac t\nMost classical local properties of a Banach spaces (for example type or cotype\, UMD) are defined in terms of the boundedness of vector-valued op erators between Lp spaces or their subspaces. It was in fact proved by Her nandez in the early 1980s that this is the case of any property that is st able by Lp direct sums and finite representability. His result can be seen as one direction of a bipolar theorem for a non-linear duality between Ba nach spaces and operators. I will present the other direction and describe the bipolar of any class of operators for this duality. The talk will be based on my recent preprint.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Johann Langemets (University of Tartu) DTSTART:20210312T150000Z DTEND:20210312T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/48 DESCRIPTION:Title: A characterization of Banach spaces containing $\\ell_1(\\k appa)$ via ball-covering properties\nby Johann Langemets (University o f Tartu) as part of Banach spaces webinars\n\n\nAbstract\nIn 1989\, G. God efroy proved that a Banach space contains an isomorphic copy of $\\ell_1$ if and only if it can be equivalently renormed to be octahedral. It is kno wn that octahedral norms can be characterized by means of covering the uni t sphere by a finite number of balls. This observation allows us to connec t the theory of octahedral norms with ball-covering properties of Banach s paces introduced by L. Cheng in 2006. Following this idea\, we extend G. G odefroy's result to higher cardinalities. We prove that\, for an infinite cardinal $\\kappa$\, a Banach space $X$ contains an isomorphic copy of $\\ ell_1(\\kappa^+)$ if and only if it can be equivalently renormed in such a way that its unit sphere cannot be covered by $\\kappa$ many open balls n ot containing $\\alpha B_X$\, where $\\alpha\\in (0\,1)$. We also investig ate the relation between ball-coverings of the unit sphere and octahedral norms in the setting of higher cardinalities. This is a joint work with S. Ciaci and A. Lissitsin.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuval Wigderson (Stanford) DTSTART:20210326T140000Z DTEND:20210326T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/49 DESCRIPTION:Title: New perspectives on the uncertainty principle\nby Yuval Wigderson (Stanford) as part of Banach spaces webinars\n\n\nAbstract\nThe phrase ``uncertainty principle'' refers to a wide array of results in sev eral disparate fields of mathematics\, all of which capture the notion tha t a function and its Fourier transform cannot both be ``very localized''. The measure of localization varies from one uncertainty principle to the n ext\, and well-studied notions include the variance (and higher moments)\, the entropy\, the support-size\, and the rate of decay at infinity. Simil arly\, the proofs of the various uncertainty principles rely on a range of tools\, from the elementary to the very deep. In this talk\, I'll describ e how many of the uncertainty principles all follow from a single\, simple result\, whose proof uses only a basic property of the Fourier transform: that it and its inverse are bounded as operators $L^1 \\to L^\\infty$. Us ing this result\, one can also prove new variants of the uncertainty princ iple\, which apply to new measures of localization and to operators other than the Fourier transform. This is joint work with Avi Wigderson.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Ferenczi (Universidade de São Paulo) DTSTART:20210409T140000Z DTEND:20210409T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/50 DESCRIPTION:Title: There is no largest proper operator ideal\nby Valentin Ferenczi (Universidade de São Paulo) as part of Banach spaces webinars\n\ n\nAbstract\nAn operator ideal $U$ (in the sense of Pietsch) is proper if \n$Space(U)$\, the class of spaces $X$ for which $Id_X \\in U$\, is reduce d to the class of finiite-dimensional spaces. Equivalently\, $U$ is proper if $U(X)$ is a proper ideal of $L(X)$ whenever $X$ is infinite dimensiona l (where $U(X)$ denotes the set of operators on $X$ which belong to $U$).\ n \nWe answer a question posed by Pietsch in 1979 by proving that there i s no largest proper operator ideal. Our proof is based on an extension of the construction by Aiena-Gonz\\'alez (2000)\, of an improjective but e ssential operator on Gowers-Maurey's shift space (1997)\, through a new an alysis of the algebra of operators on powers of the shift space.\n \nSuppo rted by FAPESP\, project 2016/25574-8\, and CNPq\, grant 303731/2019-2\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/50/ END:VEVENT BEGIN:VEVENT SUMMARY:March Boedihardjo (UCLA) DTSTART:20210423T140000Z DTEND:20210423T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/51 DESCRIPTION:Title: Spectral norms of Gaussian matrices with correlated entries \nby March Boedihardjo (UCLA) as part of Banach spaces webinars\n\n\nA bstract\nAbstract: We give a non-asymptotic bound on the spectral norm of a $d×d$\nmatrix $X$ with centered jointly Gaussian entries in terms of th e\ncovariance matrix of the entries. In some cases\, this estimate is shar p\nand removes the $\\sqrt{log d}$ factor in the noncommutative Khintchine \ninequality. Joint work with Afonso Bandeira.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Beata Randrianantoanina (Miami University in Ohio) DTSTART:20210430T140000Z DTEND:20210430T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/52 DESCRIPTION:Title: On $L_1$-embeddability of unions of $L_1$-embeddable metric spaces and of twisted unions of hypercubes\nby Beata Randrianantoanin a (Miami University in Ohio) as part of Banach spaces webinars\n\n\nAbstra ct\nLet $\\mathcal{E}$ be a class of metric spaces\, $(X\,d)$ be a metric space\, and $A\,B$ be metric subspaces of $X$ such that $X=A\\cup B$ and $ (A\,d)\, (B\,d)$ embed bilipschitzly into spaces $E_A\,E_B\\in \\mathcal{E }$ with distortions $D_A\, D_B$\, respectively. Does this imply that there exists a constant $D$ depending only on $D_A\, D_B$\, and the class $\\ma thcal{E}$\, so that $(X\,d)$ embeds bilipschitzly into some space $E_X\\in \\mathcal{E}$ with distortion $D$?\n \nThis question was answered affirma tively for the class $\\mathcal{E}$ of all ultrametric spaces by Mendel an d Naor in 2013\, and for the class $\\mathcal{E}$ of all Hilbert spaces by K. Makarychev and Y. Makarychev in 2016. K. Makarychev and Y. Makarychev in 2016 conjectured that the answer is negative when $\\mathcal{E}$ is a c lass of $\\ell_p$-spaces for any fixed $p\\notin\\{2\,\\infty\\}\,$ in par ticular for $p=1$. In this connection\, Naor in 2015 and Naor and Rabani i n 2017 asked whether the metric space known as ``twisted union of hypercub es''\, first introduced by Lindenstrauss in 1964\, and also considered by Johnson and Lindenstrauss in 1986\, embeds into $\\ell_1$.\n \n \nIn this talk I will show how to embed general classes of twisted unions of $L_1$-e mbeddable metric spaces into $\\ell_1$\, including twisted unions of hyper cubes whose metrics are determined by concave functions of the $\\ell_1$-n orm\, and discuss some related results (joint work with Mikhail I. Ostrovs kii).\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Jordi López Abad (UNED) DTSTART:20210507T140000Z DTEND:20210507T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/53 DESCRIPTION:Title: A note on Pelczynski's universal basis space\nby Jordi López Abad (UNED) as part of Banach spaces webinars\n\n\nAbstract\nWe pro ve that the isometry group of a renorming of the Pelczynski's universal ba sis space is extremely amenable. To do this\, we see that the class of fin ite dimensional normed spaces is a complemented Fraïssé class with the a pproximate Ramsey property. This is a joint work with Jamal Kawach.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Marek Cúth (Charles University in Prague) DTSTART:20210514T140000Z DTEND:20210514T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/54 DESCRIPTION:Title: Lipschitz-free $p$-spaces\nby Marek Cúth (Charles Univ ersity in Prague) as part of Banach spaces webinars\n\n\nAbstract\nAbstrac t: In a joint project with F. Albiac\, J. L. Ansorena and M. Doucha we hav e been recently investigating the class of Lipschitz-free p-Banach spaces\ , which is a generalization of the concept of the nowadays quite attractiv e class of Lipschitz-free spaces (which is covered by the case of $p=1$). In order to obtain reasonable generalizations from the case of $p=1$ to th e case of $0\\lt p\\le 1$\, we had to develop new techniques which were le ading also to new results for the classical case of $p=1$. In the talk I w ould like to survey our results from 5 papers which we produced during las t 2 years.\n\nA special emphasis will be given to the result contained in our last paper where we prove that for any metric space $M$ there exists a bounded metric space $B(M)$ which is topologically homeomorphic to $M$ su ch that Lipschitz-free $p$-spaces over $M$ and $B(M)$ are linearly isomorp hic for every $0\\lt p\\le 1$. This particular result is new even for the classical case of $p=1$ and as a consequence it provides us a very natural multiplication on the space of Lipschitz functions over any metric space (even unbounded one) such that this space becomes a Banach algebra.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Hugh Wark (York\, England) DTSTART:20210521T140000Z DTEND:20210521T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/55 DESCRIPTION:Title: Equilateral sets in large Banach spaces\nby Hugh Wark ( York\, England) as part of Banach spaces webinars\n\n\nAbstract\nA subset of a Banach space is called equilateral if the distances between any two o f its distinct points are the same. In this talk it will be shown that the re exist non separable Banach spaces with no uncountable equilateral sets and indeed non separable Banach spaces with no infinite equilateral sets.\ n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Harrison H. Gaebler (University of Kansas) DTSTART:20210528T140000Z DTEND:20210528T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/56 DESCRIPTION:Title: Asymptotic Geometry of Banach Spaces that have a Well-Behav ed Riemann Integral\nby Harrison H. Gaebler (University of Kansas) as part of Banach spaces webinars\n\n\nAbstract\nBanach spaces for which Riem ann integrability implies Lebesgue almost everywhere continuity are said t o have the Property of Lebesgue\, or to be ``PL-spaces." It is an open pro blem to derive a full characterization of PL-spaces. In this talk\, I will first give a brief overview of Riemann and Darboux integrability for Bana ch-valued functions\, and I will then introduce the Property of Lebesgue w ith some relevant examples. I will next show how the Property of Lebesgue is connected to the asymptotic geometry (both global and local) of the und erlying Banach space\, and I will present three new results in this direct ion that are to appear later this year in Real Analysis Exchange. Finally\ , I will discuss two possibilities for future research on characterizing P L-spaces\, and a connection between the Property of Lebesgue and the disto rtion of the unit sphere as well.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Yoël Perreau (Besançon) DTSTART:20210625T140000Z DTEND:20210625T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/57 DESCRIPTION:by Yoël Perreau (Besançon) as part of Banach spaces webinars \n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Henrik Johannes Wirzenius (University of Helsinki) DTSTART:20210702T140000Z DTEND:20210702T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/58 DESCRIPTION:Title: Closed ideals in the algebra of compact-by-approximable ope rators\nby Henrik Johannes Wirzenius (University of Helsinki) as part of Banach spaces webinars\n\n\nAbstract\nIn this talk I will present vario us examples of non-trivial closed ideals of the compact-by-approximable qu otient algebra $\\mathfrak A_X=\\mathcal K(X)/\\mathcal A(X)$ on Banach sp aces $X$ failing the approximation property. Here $\\mathcal K(X)$ denotes the algebra of compact operators $X\\to X$ and $\\mathcal A(X)=\\overline {\\mathcal F(X)}$ is the uniform norm closure of the bounded finite rank o perators $\\mathcal F(X)$.\n\nThe examples include:\n\n(i) If $X$ has coty pe 2\, $Y$ has type 2\, $\\mathfrak A_X\\neq\\{0\\}$ and $\\mathfrak A_Y\\ neq\\{0\\}$\, then $\\mathfrak A_{X\\oplus Y}$ has at least 2 (and in some cases up to 8) closed ideals. \n\n(ii) For all $4\\lt p\\lt \\infty$ the re are closed subspaces $X\\subset\\ell^p$ and $X\\subset c_0$ such that $ \\mathfrak A_X$ has a non-trivial closed ideal.\n\n(iii) A Banach space $Z $ such that $\\mathfrak A_Z$ contains an uncountable lattice of closed ide als.\n\nThe talk is based on a recent preprint [arXiv:2105.08403] together with Hans-Olav Tylli (University of Helsinki).\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Lindemulder and Emiel Lorist (Karlsruhe Institute of Technolo gy and University of Helsinki) DTSTART:20210618T140000Z DTEND:20210618T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/59 DESCRIPTION:Title: A discrete framework for interpolation of Banach spaces \nby Nick Lindemulder and Emiel Lorist (Karlsruhe Institute of Technology and University of Helsinki) as part of Banach spaces webinars\n\n\nAbstrac t\nWe develop a discrete framework for the interpolation of Banach spaces\ , which contains e.g. the well-known real and complex interpolation method s\, but also more exotic methods like the $\\pm$-method\, the Radamacher i nterpolation method and the $\\ell^p$-interpolation method\, as concrete e xamples. Our method is based on a sequential structure imposed on a Banach space and has both a formulation modelled after the real and the complex interpolation methods.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Rubén Medina (University of Granada) DTSTART:20210716T140000Z DTEND:20210716T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/60 DESCRIPTION:Title: Compact retractions and the $\\pi$-property of Banach spac es\nby Rubén Medina (University of Granada) as part of Banach spaces webinars\n\n\nAbstract\nIn the talk we will focus on Lipschitz retractions of a separable \nBanach space $X$ onto its closed and convex generating s ubsets $K$\, a \nquestion asked by Godefroy and Ozawa in 2014. Our results are concerning \nthe case when $K$ is in some quantitative sense small\, namely when $K$ \nis in very little neibourhoods of certain finite dimensi onal sections of \nit. Under such assumptions we obtain a near characteriz ation of the \n$\\pi$-property (resp. Finite Dimensional Decomposition pro perty) of a \nseparable Banach space $X$. In one direction\, if $X$ admits the Finite \nDimensional Decomposition (which is isomorphically equivalen t to the \nmetric-$\\pi$-property) then we will see how to construct a Lip schitz \nretraction onto a (small) generating convex compact $K$. On the o ther \nhand\, we will prove that if $X$ admits a small (in a precise sense ) \ngenerating compact Lipschitz retract then $X$ has the $\\pi$-property. It \nseems to be an open problem whether the $\\pi$-property is isomorphi cally \nequivalent to the metric-$\\pi$-property (a positive answer would turn \nour results into a complete characterization). In the case of dual \nBanach spaces\, this characterization is indeed valid.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Miguel Berasategui (University of Buenos Aires) DTSTART:20210709T140000Z DTEND:20210709T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/61 DESCRIPTION:Title: Bidemocratic bases and their connections with other greedy- type bases\nby Miguel Berasategui (University of Buenos Aires) as part of Banach spaces webinars\n\n\nAbstract\nIn this talk we will focus on bi democratic bases of Banach and quasi-Banach spaces\, and their greedy-like properties. In particular\, we will address the relation between bidemocr atic bases and quasi-greedy bases. On the one hand\, there are subspaces o f $\\ell_p$ with bidemocratic bases that are not quasi-greedy. On the othe r hand\, for every arbitrary fundamental function $\\varphi$\, there is a Banach space with a bidemocratic\, quasi-greedy conditional Schauder basis whose fundamental funcion grows as $\\varphi$.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavlos Motakis (York University) DTSTART:20211015T140000Z DTEND:20211015T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/62 DESCRIPTION:Title: Separable spaces of continuous functions as Calkin algebras \nby Pavlos Motakis (York University) as part of Banach spaces webinar s\n\n\nAbstract\nThe Calkin algebra $\\mathcal{C}al(X)$ of a Banach space $X$ is the quotient algebra of all bounded linear operators $\\mathcal{L}( X)$ on $X$ over the ideal of all compact ones $\\mathcal{K}(X)$. A questio n that has gathered attention in recent years is what unital Banach algebr as admit representations as Calkin algebras. There is a strong connection between quotients algebras of $\\mathcal{L}(X)$ and the tight control of t he operators on $X$ modulo a small ideal. We discuss a new contribution to this topic\, namely that for every compact metric space $K$ there exists a Banach space $X$ so that $\\mathcal{C}al(X)$ coincides isometrically wit h $C(K)$ as a Banach algebra.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Abraham Rueda Zoca (Universidad de Murcia) DTSTART:20211105T140000Z DTEND:20211105T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/63 DESCRIPTION:Title: $L$-orthogonal elements and spaces of operators\nby Abr aham Rueda Zoca (Universidad de Murcia) as part of Banach spaces webinars\ n\n\nAbstract\nGiven a Banach space $X$\, we say that an element $u\\in X^ {**}$ is $L$-orthogonal if\, for every $x\\in X$\, it follows that\n$$\\Ve rt x+u\\Vert=\\Vert x\\Vert+\\Vert u\\Vert.$$\nIn 1989\, G. Godefroy prove d that a Banach space $X$ admits an equivalent renorming with non-zero $L$ -orthogonal elements if\, and only if\, $X$ contains an isomorphic copy of $\\ell_1$. Moreover\, G. Godefroy and N. J. Kalton proved (in 1989 too) t hat a separable space $X$ has non-zero $L$-orthogonal elements if\, and on ly if\, the following condition holds:\n\\begin{center}\nFor every finite- dimensional subspace $F$ of $X$ and every $\\varepsilon>0$ there exists $x \\in S_X$ so that $\\Vert y+\\lambda x\\Vert\\geq (1-\\varepsilon)(\\Vert y\\Vert+\\vert\\lambda\\vert)$ holds for every $y\\in F$ and every $\\lamb da\\in\\mathbb R$.\n\\end{center}\n\nIn this talk we will examine the vali dity of this theorem for non-separable Banach spaces. For this\, and for o ther results of the structure of the set of $L$-orthogonal elements\, the Banach spaces of linear bounded operators between two Banach spaces will p lay a crucial role.\n\n\n\nThe author was supported by Juan de la Cierva-F ormaci\\'on fellowship FJC2019-039973\, by MTM2017-86182-P (Government of Spain\, AEI/FEDER\, EU)\, by MICINN (Spain) Grant PGC2018-093794-B-I00 (MC IU\, AEI\, FEDER\, UE)\, by Fundaci\\'on S\\'eneca\, ACyT Regi\\'on de Mur cia grant 20797/PI/18\, by Junta de Andaluc\\'ia Grant A-FQM-484-UGR18 and by Junta de Andaluc\\'ia Grant FQM-0185.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Florent Baudier (Texas A&M) DTSTART:20211112T150000Z DTEND:20211112T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/64 DESCRIPTION:Title: Umbel convexity and the geometry of trees\nby Florent B audier (Texas A&M) as part of Banach spaces webinars\n\n\nAbstract\nMarkov convexity is a powerful invariant\, introduced by Lee\, Naor and Peres mo re than 15 years ago\, which is related to the geometry of (locally finite ) trees and (quantitative) uniformly convex renormings.\nIn a joint work w ith Chris Gartland we introduced new metric invariants capturing the geome try of countably branching trees. Our main invariant\, called umbel convex ity\, was inspired by Markov convexity and shares many of its desirable fe atures. Most notably\, it provides lower bounds on the distortion/compress ion required when embedding countably branching trees\, and it is stable u nder certain nonlinear quotients. I will explain the close relationship be tween umbel convexity and Rolewicz's property $\\beta$ renormings. If time permits\, I will discuss the notion of umbel cotype\, a relaxation of umb el convexity\, and its relevance to the geometry of Heisenberg groups.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Krzsystof Swiecicki (Texas A&M) DTSTART:20211119T150000Z DTEND:20211119T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/65 DESCRIPTION:Title: No dimension reduction for doubling spaces of $\\ell_q$ for $q>2$.\nby Krzsystof Swiecicki (Texas A&M) as part of Banach spaces w ebinars\n\n\nAbstract\nWe'll provide a new elementary proof for the imposs ibility of dimension reduction for doubling subsets of $\\ell_q$ for $q>2$ . This is done by constructing a family of diamond graph-like objects base d on the construction by Bartal\, Gottlieb\, and Neiman. We'll compare our approach with previous results and discuss their advantages and disadvant ages. One noteworthy consequence of our proof is that it can be naturally generalized to obtain embeddability obstructions into non-positively curve d spaces or asymptotically uniformly convex Banach spaces. Based on the wo rk with Florent Baudierabd Andrew Swift.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Kasia Wyczesany (Tel Aviv) DTSTART:20211203T150000Z DTEND:20211203T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/66 DESCRIPTION:Title: On almost Euclidean and well-complemented subspaces of fini te-dimensional normed spaces\nby Kasia Wyczesany (Tel Aviv) as part of Banach spaces webinars\n\n\nAbstract\nIn this talk I will discuss a versi on of an old question of Vitali Milman about almost Euclidean and well-com plemented subspaces. In particular\, I will introduce a notion of ' ε-goo d points '\, which allows for a convenient reformulation of the problem. L et (X\,||·||X) be a normed space. It turns out that if a linear subspace Y ⊂ X consists entirely of ε-good points then the restriction of the no rm ||·||X to Y must be approximately a multiple of the l2 norm and the op erator norm of the orthogonal projection onto Y is close to 1. I will pres ent an example of a normed space X of arbitrarily high dimension\, whose B anach-Mazur distance from the l2dim X is at most 2\, but such that non of its (even two-dimensional) subspaces consists entirely of ε-good points. The talk is based on joint work with Timothy Gowers.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Gartland (Texas A&M) DTSTART:20211210T150000Z DTEND:20211210T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/67 DESCRIPTION:by Chris Gartland (Texas A&M) as part of Banach spaces webinar s\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Ostrovskii (St. John's University) DTSTART:20220304T150000Z DTEND:20220304T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/68 DESCRIPTION:Title: Dvoretzky-type theorem for locally finite subsets of a Hilb ert space\nby Mikhail Ostrovskii (St. John's University) as part of Ba nach spaces webinars\n\n\nAbstract\nThe main result of the talk: Given an y $\\varepsilon>0$\, every locally finite subset of $\\ell_2$ admits a $(1 +\\varepsilon)$-bilipschitz embedding into an arbitrary infinite-dimension al Banach space.\n\n \nThe result is based on two results which are of ind ependent interest:\n\n \n(1) A direct sum of two finite-dimensional Euclid ean spaces contains a sub-sum of a controlled dimension which is $\\vareps ilon$-close to a direct sum with respect to a $1$- unconditional basis in a two-dimensional space.\n\n \n(2) For any finite-dimensional Banach space $Y$ and its direct sum $X$ with itself with respect to a $1$-unconditiona l basis in a two-dimensional space\, there exists a $(1+\\varepsilon)$-bil ipschitz embedding of $Y$ into $X$ which on a small ball coincides with th e identity map onto the first summand and on a complement of a large ball coincides with the identity map onto the second summand.\n\n\n(joint with F. Catrina and S. Ostrovska)\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Jarosław Swaczyna (Technical University of Łódź) DTSTART:20220422T140000Z DTEND:20220422T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/69 DESCRIPTION:Title: Continuity of coordinate functionals for filter Schauder ba sis\nby Jarosław Swaczyna (Technical University of Łódź) as part o f Banach spaces webinars\n\n\nAbstract\nGiven a filter of subsets of natur al numbers $F$ we say that a sequence $(x_n)$ is $F$-convergent to $x$ if for every $\\varepsilon>0 $condition $\\{n\\in \n:d(x_n\,x)<\\varepsilon \ \}\\in F$ holds. We may use this notion to generalize the idea of Schauder basis\, namely we say that a sequence $(e_n)$ is an $F$-basis if for ever y $x\\in X$ there exists a unique sequence of scalars $(\\alpha_n)$ s.t. $ \\sum_{n\,F} \\alpha_n e_n=x$\, which means that the sequence of partial s ums is $F$-convergent to $x$. Once such a notion is introduced it is natur al to ask whenever corresponding coordinate functionals are continuous. Su ch a question was posed by V. Kadets during the 4th conference Integration \, Vector Measures\, and Related Topics held in 2011 in Murcia. Surprising ly\, there is an obstacle related to the lack of uniform boundedness of fu nctionals related to $F$ basis\, due to which we can not find proof of con tinuity analogous to the classical case. During my talk\, I will discuss t he problem and provide two proofs of continuity of considered functionals\ , which uses under some large cardinal assumptions. This is joint work wit h Tomasz Kania and Noe de Rancourt\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Doležal (The Czech Academy of Sciences) DTSTART:20220520T140000Z DTEND:20220520T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/70 DESCRIPTION:Title: Descriptive complexity of Banach spaces\nby Martin Dole žal (The Czech Academy of Sciences) as part of Banach spaces webinars\n\n \nAbstract\nWe introduce a new natural coding of separable Banach spaces.\ nThe set of codes consists of (pseudo)norms on a certain vector space and is equipped with a canonical Polish topology.\nWe use this coding to inves tigate the descriptive complexities of some classical Banach spaces.\nAmon g other results\, we show that $\\ell_2$ is\n\n\na) the unique (up to isom etry) separable Banach space with a closed isometry class\,\n\nb) the uniq ue (up to isomorphism) separable Banach space with an $F_\\sigma$ isomorph ism class.\n\n\nThis is a joint work with Marek C\\'uth\, Michal Doucha an d Ond\\v rej Kurka.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Hung Viet Chu (UIUC) DTSTART:20220930T140000Z DTEND:20220930T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/71 DESCRIPTION:Title: A Relaxation of Optimality for the TGA\nby Hung Viet Ch u (UIUC) as part of Banach spaces webinars\n\n\nAbstract\nWe begin by reca lling the Thresholding Greedy Algorithm (TGA) introduced by Konyagin and T emlyakov in 1999. The TGA optimality is described by the notion of greedy and almost greedy bases.\nA basis $(e_n)_{n=1}^\\infty$ of a Banach space $X$ (over a field $\\mathbb{F}$) is said to be greedy if there exists a co nstant $\\mathbf C\\geqslant 1$ such that \n\n$$\\|x-G_m(x)\\|\\ \\leqslan t\\ \\mathbf C\\inf_{\\substack{|A|\\leqslant m\\\\(a_n)_{n\\in A}\\subset \\mathbb{F}}}\\left\\|x-\\sum_{n\\in A}a_ne_n\\right\\|.$$\n\nHere\, $G_m (x)$ is the so-called greedy sum of $x$ of size $m$. The definition of al most greedy bases replaces the arbitrary linear combinations on the right by projections. \nWe present properties of both greedy and almost bases as well as their characterizations. \n\nExtending classical results\, we def ine ($f$\, greedy) bases to satisfy the condition: there exists a constant $\\mathbf C\\geqslant 1$ such that \n\n$$\\|x-G_m(x)\\|\\ \\leqslant\\ \\ mathbf C\\inf_{\\substack{|A|\\leqslant f(m)\\\\(a_n)_{n\\in A}\\subset \\ mathbb{F}}}\\left\\|x-\\sum_{n\\in A}a_ne_n\\right\\|\,$$\n\nwhere $f$ bel ongs to $\\mathcal{F}$\, a collection that contains functions like $f(x) = cx^{\\gamma}$ for $c\, \\gamma\\in [0\,1]$. The definition of ($f$\, almo st greedy) is modified accordingly. We give characterizations of these bas es\, which help establish the surprising equivalence: if $f$ is a non-iden tity function in $\\mathcal{F}$\, then a basis is ($f$\, greedy) if and on ly if it is ($f$\, almost greedy). We show that ($f$\, greedy) bases form a much wider class as there exist examples of classical bases that are not almost greedy but is ($f$\, greedy) for some $f\\in\\mathcal{F}$.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Freeman (St Louis University) DTSTART:20230210T150000Z DTEND:20230210T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/72 DESCRIPTION:Title: Stable phase retrieval in function spaces\, Part I\nby Daniel Freeman (St Louis University) as part of Banach spaces webinars\n\n \nAbstract\nLet $(\\Omega\,\\Sigma\,\\mu)$ be a measure space\, and $1\\le q p\\leq \\infty$. A subspace $E\\subseteq L_p(\\mu)$ is said to do stable phase retrieval (SPR) if there exists a constant $C\\geq 1$ such that for any $f\,g\\in E$ we have \n$$\\inf_{|\\lambda|=1} \\|f-\\lambda g\\|\\leq C\\||f|-|g|\\|.$$\n In this case\, if $|f|$ is known\, then $f$ is un iquely determined up to an unavoidable global phase factor $\\lambda$\; mo reover\, the phase recovery map is $C$-Lipschitz. Phase retrieval appears in several applied circumstances\, ranging from crystallography to quantum mechanics.\n\n\nWe will discuss how problems in phase retrieval are natur ally related to classical notions in the theory of Banach lattices. Throug h making this connection\, we may apply established methods from the subje ct to attack problems in phase retrieval\, and conversely we hope that the ideas and questions in phase retrieval will inspire a new avenue of resea rch in the theory of Banach lattices.\n\nThis talk is based on joint work with Benjamin Pineau\, Timur Oikhberg\, and Mitchell Taylor.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Mitchell A. Taylor (UC Berkeley) DTSTART:20230217T150000Z DTEND:20230217T160000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/73 DESCRIPTION:Title: Stable phase retrieval in function spaces\, Part II\nby Mitchell A. Taylor (UC Berkeley) as part of Banach spaces webinars\n\n\nA bstract\nLet $(\\Omega\,\\Sigma\,\\mu)$ be a measure space\, and $1\\leq p \\leq \\infty$. A subspace $E\\subseteq L_p(\\mu)$ is said to do stable ph ase retrieval (SPR) if there exists a constant $C\\geq 1$ such that for an y $f\,g\\in E$ we have \n $$\\inf_{|\\lambda|=1} \\|f-\\lambda g\\|\\le q C\\||f|-|g|\\|.$$\n In this case\, if $|f|$ is known\, then $f$ is u niquely determined up to an unavoidable global phase factor $\\lambda$\; m oreover\, the phase recovery map is $C$-Lipschitz. Phase retrieval appears in several applied circumstances\, ranging from crystallography to quantu m mechanics.\n\n\nIn this talk\, I will present some elementary examples o f subspaces of $L_p(\\mu)$ which do stable phase retrieval\, and discuss t he structure of this class of subspaces. This is based on a joint work wit h M. Christ and B. Pineau\, as well as a joint work with D. Freeman\, B. P ineau and T. Oikhberg.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Kamil Krzysztof Ryduchowski (Warsaw) DTSTART:20230324T140000Z DTEND:20230324T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/74 DESCRIPTION:Title: Equilateral and separated sets in some nonseparable Banach spaces\nby Kamil Krzysztof Ryduchowski (Warsaw) as part of Banach spac es webinars\n\n\nAbstract\nA subset $S$ of a Banach space $X$ is called $r $-equilateral (resp.\, $r$-separated) if any two points of $S$ are in the distance exactly $r$ (resp.\, at least $r$) from each other. Whereas Teren zi constructed an infinite-dimensional Banach space without infinite equil ateral sets\, Elton and Odell proved that the unit sphere of every infinit e-dimensional Banach space contains an infinite $(1+r)$-separated set for some $r>0$. Recently\, some research has been done concerning the uncounta ble versions of these problems\, e.g.\, Kania\, Hajek and Russo proved tha t the unit sphere of every nonseparable reflexive Banach spaces contains a n uncountable $(1+r)$-separated set for some $r>0$. \n\nDuring my talk\, I will present some known results concerning this line of research and disc uss joint results with Piotr Koszmider. In particular\, I will show that\, under some set-theoretic assumptions\, there is an equivalent renorming o f the nonseparable Hilbert space $\\ell_2(\\omega_1)$ without uncountable equilateral sets.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Rosendal (The University of Maryland) DTSTART:20230421T140000Z DTEND:20230421T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/75 DESCRIPTION:Title: On the relation of coarse embeddability between Banach spac es\nby Christian Rosendal (The University of Maryland) as part of Bana ch spaces webinars\n\n\nAbstract\nUnder the weak assumption on a Banach sp ace $E$ that $E\\oplus E$ embeds isomorphically into $E$\, we provide a ch aracterisation of when a Banach space $X$ coarsely embeds into $E$ via a s ingle numerical invariant.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruce Blackadar (University of Nevada\, Reno) DTSTART:20230512T140000Z DTEND:20230512T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/76 DESCRIPTION:Title: Hilbert Spaces Without Countable AC\nby Bruce Blackadar (University of Nevada\, Reno) as part of Banach spaces webinars\n\n\nAbst ract\nThis article examines Hilbert spaces constructed from sets whose exi stence is incompatible with the Countable Axiom of Choice (CC). Our point of view is twofold: (1) We examine what can and cannot be said about Hilbe rt spaces and operators on them in ZF set theory without any assumptions o f Choice axioms\, even the CC. (2) We view Hilbert spaces as ``quantized'' sets and obtain some set-theoretic results from associated Hilbert spaces .\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Pelczar-Barwacz (Jagiellonian University) DTSTART:20230505T140000Z DTEND:20230505T150000Z DTSTAMP:20260404T094656Z UID:BanachWebinars/77 DESCRIPTION:Title: A Banach space with an infinite dimensional reflexive quoti ent operator algebra $L(X)/SS(X)$\nby Anna Pelczar-Barwacz (Jagielloni an University) as part of Banach spaces webinars\n\n\nAbstract\nI will dis cuss method of constructing a Banach space $X$ such that the algebra of bo unded operators $L(X)$ is a direct sum of an infinite dimensional reflexiv e Banach space $V$ and the operator ideal of strictly singular operators $ SS(X)$. \nThe space $V$ is spanned by an unconditional basic sequence $(I_ s)_{s=0}^\\infty$ where $I_0$ is the identity on $X$\, whereas each $I_s\, s=1\,2\,...$ is a projection on some subspace $X_s$ of $X$. The multiplic ation on $V$ is defined naturally: $V$ is the unitization of the subalgebr a of $L(X)$ spanned by $(I_s)_{s=1}^\\infty$ with the pointwise multiplica tion.\n LOCATION:https://stable.researchseminars.org/talk/BanachWebinars/77/ END:VEVENT END:VCALENDAR