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BEGIN:VEVENT
SUMMARY:Chi-Kwong Li (College of William and Mary\, Virginia)
DTSTART:20200529T150000Z
DTEND:20200529T160000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/1
DESCRIPTION:Title: Quantum states and quantum channels\nby Chi-Kwong Li (
College of William and Mary\, Virginia) as part of Preserver Webinar\n\n\n
Abstract\nIn the Hilbert space formulation\, quantum states are density ma
trices\, i.e.\, positive semidefinite matrices with trace one\, and quantu
m channels are trace preserving completely positive linear maps on matrice
s. In this talk\, we will present some results on the existence of quantum
channels with some special properties. Open problems in constructing spec
ial types of quantum channel will be mentioned.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lajos Molnár (University of Szeged)
DTSTART:20200605T110000Z
DTEND:20200605T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/2
DESCRIPTION:Title: Means and their preservers\nby Lajos Molnár (Universi
ty of Szeged) as part of Preserver Webinar\n\n\nAbstract\nIn this talk we
survey our recent work on preservers related to operator means.\n\nWe deal
with morphisms with respect to means as operations on positive definite o
r semidefinite cones in operator algebras and consider preservers of norms
of means in similar settings. The first group of questions are motivated
by the study of certain isometries while the second group of problems have
a loose connection to quantum mechanical symmetry transformations. We dis
cuss possibilities of transforming one mean to another one and\, if time p
ermits\, we also present some characterizations of specific means.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Peralta (University of Granada)
DTSTART:20200612T150000Z
DTEND:20200612T160000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/3
DESCRIPTION:Title: Tingley's problem for subsets strictly smaller than the un
it sphere\nby Antonio Peralta (University of Granada) as part of Prese
rver Webinar\n\n\nAbstract\nThe celebrated Tingley's problem has focused t
he attention of a wide community of researchers on preservers in recent ye
ars. It admits the following easy statement: Suppose $\\Delta : S(X) \\to
S(Y)$ is a surjective isometry between the unit spheres of two Banach spac
es $X$ and $Y$. Does $\\Delta$ admit an extension to a surjective linear i
sometry from $X$ onto $Y$? This difficult problem remains open even in the
case of 2-dimensional spaces. A long series of papers has been devoted to
provide positive answers for some concrete structures\, these partial ans
wers have produced a wide range of new tools and results with interesting
geometric and analytic conclusion.\n\n\nThe reader might guess from the ti
tle that we won't limit ourself to Tingley's problem in this talk. It is n
atural to challenge the audience to consider other variants. We shall deal
with one of the most attractive and we shall consider the posibility of e
xtending surjective isometries between proper subsets of the unit spheres
(for example\, the subset of extreme points of the closed unit ball\, the
subset of positive elements in the unit sphere of $B(H)$\, the subgroup of
unitary elements in a unital C$^*$-algebra\, the set of unitary elements
in a unital JB$^*$-algebra\, etcetera). We shall see that negative and pos
itive answers can be obtained.\n\n\n[1] M. Cueto-Avellaneda\, A.M. Peralta
\, The Mazur--Ulam property for commutative von Neumann algebras\, Linear
and Multilinear Algebra\, 68\, No. 2\, 337--362 (2020).\n\n \n[2] M. Cu
eto-Avellaneda\, A.M. Peralta\, Can one identify two unital JB$^*$-algebra
s by the metric spaces determined by their sets of unitaries?\, preprint 2
020\, arXiv:2005.04794\n\n[3] O. Hatori\, L. Molnar\, Isometries of the un
itary groups and Thompson isometries of the spaces of invertible positive
elements in C*-algebras\, J. Math. Anal. Appl.\, 409\, 158-167 (2014).\n\n
[4] G. Nagy\, Isometries of spaces of normalized positive operators under
the operator norm\, Publ. Math. Debrecen\, 92\, no. 1-2\, 243-254 (2018).\
n\n[5] A.M. Peralta\, A survey on Tingley's problem for operator algebras\
, Acta Sci. Math. (Szeged)\, 84\, 81-123 (2018).\n\n[6] A.M. Peralta\, Cha
racterizing projections among positive operators in the unit sphere\, Adv.
Oper. Theory\, 3\, no. 3\, 731-744 (2018).\n\n[7] A.M. Peralta\, On the u
nit sphere of positive operators\, Banach J. Math. Anal.\, 13\, no. 1\, 91
-112 (2019).\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matej Bresar (University of Ljubljana and University of Maribor)
DTSTART:20200617T110000Z
DTEND:20200617T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/4
DESCRIPTION:Title: Zero product determined algebras and commutativity preserv
ers\nby Matej Bresar (University of Ljubljana and University of Maribo
r) as part of Preserver Webinar\n\n\nAbstract\nA (not necessarily associat
ive) algebra $A$ over a field $F$ is said to be zero product determined if
every bilinear\nfunctional $f : A \\times A \\to F$ with the property t
hat $ab = 0$ implies $f(a\, b) = 0$ is of the form $f(a\, b) = \\varphi(a
b)$ for some\nlinear functional $\\varphi$ on $A$.\n\nIn the context of\nB
anach algebras\, one adds the assumption that $f$ and $\\varphi$ are cont
inuous. We will first survey the general theory of zero product determined
algebras\, and then discuss its applications to commutativity preserving
linear maps.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michiya Mori (University of Tokyo)
DTSTART:20200624T110000Z
DTEND:20200624T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/5
DESCRIPTION:Title: Lattice isomorphisms between projection lattices of von Ne
umann algebras\nby Michiya Mori (University of Tokyo) as part of Prese
rver Webinar\n\n\nAbstract\nA von Neumann algebra is a weak operator close
d *-subalgebra of B(H)\,\nwhose study was initiated by Murray and von Neum
ann in 1930’s. The\ncollection of projections of a von Neumann algebra f
orms a lattice\, and\nits geometry has played a very important role in und
erstanding the\nstructure of von Neumann algebras for more than 80 years.\
n\n\nIn this talk\, we consider the following fundamental question: What i
s\nthe general form of lattice isomorphisms between projection lattices of
\nvon Neumann algebras? Von Neumann gave an answer to this question for\nt
ype $\\mathrm{II}_1$ factors. He proved that a lattice isomorphism can be
described\nby means of a ring isomorphism between the algebras of affiliat
ed\noperators. However\, apparently no answer to this question has been gi
ven\nfor the general case (in particular for type $\\mathrm{III}$ von Neum
ann algebras)\nuntil now. In this talk\, we begin with a brief recap of th
e classical\ntheory of von Neumann algebras\, and then give an answer to o
ur question\nfor general von Neumann algebras (save type $\\mathrm{I}_1$ a
nd $\\mathrm{I}_2$) using ring\nisomorphisms between the algebras of local
ly measurable operators. We\nalso consider a better description of ring is
omorphisms between locally\nmeasurable operator algebras\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Semrl (University of Ljubljana)
DTSTART:20200701T110000Z
DTEND:20200701T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/6
DESCRIPTION:Title: Loewner's theorem for maps on operator domains\nby Pet
er Semrl (University of Ljubljana) as part of Preserver Webinar\n\n\nAbstr
act\nThe classical Loewner's theorem states that operator monotone functio
ns on real intervals are described by holomorphic functions on the upper h
alf-plane. We prove an analogue where real intervals are replaced by opera
tor domains\, operator monotone functions by local order isomorphisms\, an
d upper half-plane by the set of all bounded operators whose imaginary par
t is a positive invertible operator. We will present several results on lo
cal order isomorphisms and pay a special attention to the finite-dimension
al case. This is a report on a joint work with Michiya Mori.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bas Lemmens (University of Kent)
DTSTART:20200708T110000Z
DTEND:20200708T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/7
DESCRIPTION:Title: A metric version of a theorem by Poincaré\nby Bas Lem
mens (University of Kent) as part of Preserver Webinar\n\n\nAbstract\nNume
rous theorems in several complex variables are instances of results in met
ric geometry. In this talk we shall see that a classic theorem due to Poi
ncare\, which says that there is no biholomorphic map from the polydisc on
to the (open) Euclidean ball in $C^n$ if n is at least $2$\, is a case in
point. In fact\, it is known that exists no surjective Kobayashi distance
isometry between these two domains.\n\nIn the talk we shall see how Poinc
are's theorem can be derived from a result for products of proper geodesi
c metric spaces. In fact\, the main goal of the talk is to present a gene
ral criterion\, in terms of certain asymptotic geometric properties of the
individual metric spaces\, that yields an obstruction for the existence o
f an isometric embedding between product metric spaces.\n\nThe key concept
s from metric geometry involved are: the horofunction boundary of metric
spaces\, the Busemann points\, and the detour distance. These concepts can
\, and have been\, successfully used to analyse preserver problems involvi
ng isometries.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denny H. Leung (National University of Singapore)
DTSTART:20200715T110000Z
DTEND:20200715T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/8
DESCRIPTION:Title: Nonlinear biseparating maps\nby Denny H. Leung (Nation
al University of Singapore) as part of Preserver Webinar\n\n\nAbstract\nLe
t $X\,Y$ be topological spaces and $E$\, $F$ be normed spaces. Suppose th
at $A(X\,E)$ is a vector subspace of $C(X\,E)$ (space of $E$-valued contin
uous functions on $X$) and $A(Y\,F)$ is a subspace of $C(Y\,F)$.\nAn addit
ive map $T: A(X\,E)\\to A(Y\,F)$ is {\\em disjointness preserving} if \n\\
[ \\|f(x)\\|\\cdot\\|g(x)\\| =0 \\text { for all $x\\in X$ } \\implies \\
|Tf(y)\\|\\cdot\\|Tg(y)\\| =0 \\text { for all $y\\in Y$. }\n\\]\n$T$ is {
\\em biseparating} if it is a bijection and both $T$ and $T^{-1}$ are dis
jointness preserving.\nIn this talk\, I will propose a definition of ``b
iseparating'' for general nonlinear mappings. \nThen we will proceed to an
alyze the structure of biseparating maps acting on various types of functi
on spaces (spaces of continuous functions\, uniformly continuous functions
\, Lipschitz functions\, etc).\n\n\n\n\\bigskip\n\n\n\nPart of the talk is
based on the PhD thesis of Xianzhe Feng\, completed at NUS in 2018.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javad Mashreghi (Laval University)
DTSTART:20200722T150000Z
DTEND:20200722T160000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/9
DESCRIPTION:Title: On Gleason-Kahane-Zelazko Theorems\nby Javad Mashreghi
(Laval University) as part of Preserver Webinar\n\n\nAbstract\nLet $T: H^
p \\to H^p$ be a linear mapping (no continuity assumption). What can we sa
y about $T$ if we assume that ``it preserves outer functions''? Another re
lated question is to consider linear functionals $T: H^p \\to \\mathbb{C}$
(again\, no continuity assumption) and ask about those functionals whose
kernels do not include any outer function. We study such questions via an
abstract result which can be interpreted as the generalized Gleason--Kahan
e--\\.Zelazko theorem for modules. In particular\, we see that continuity
of endomorphisms and functionals is a part of the conclusion. We go furthe
r and also discuss GKZ in other function spaces\, e.g.\, Bergman\, Dirichl
et\, Besov\, the little Bloch\, and VMOA and even generally in RKHS.\n\nTh
is is a joint work with T. Ransford.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ying-Fen Lin (Queens University Belfast)
DTSTART:20200729T110000Z
DTEND:20200729T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/10
DESCRIPTION:Title: Schur multipliers and positive extensions\nby Ying-Fe
n Lin (Queens University Belfast) as part of Preserver Webinar\n\n\nAbstra
ct\nThe positive completion problem for a partially defined matrix asks wh
en the unspecified entries can be determined in such a way that the result
ing fully defined matrix is positive semi-definite. The problem has attrac
ted a considerable attention in the literature\, and had been studied usin
g combinatorial approaches\, until Paulsen\, Power and Smith observed in t
he late 1980's that it is closely related to completely positive maps and
operator systems. \n\nIn this talk\, after presenting an overview of the c
lassical problem\, I will discuss an infinite dimensional and continuous s
etting\, where finite matrices are replaced by measurable Schur multiplier
s. I will first introduce scalar-valued and operator-valued Schur multipli
ers and their partially defined versions\, and present a Grothendieck-type
characterisation of operator-valued Schur multipliers. Then I will talk a
bout the positive extension problem of Schur multipliers and characterise
its affirmative solution in terms of structures on an operator system asso
ciated with the domain of the Schur multipliers.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osamu Hatori (Niigata University)
DTSTART:20200805T110000Z
DTEND:20200805T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/11
DESCRIPTION:Title: When does an isometry on a Banach algebra preserve the mu
ltiplicative structure?\nby Osamu Hatori (Niigata University) as part
of Preserver Webinar\n\n\nAbstract\nThe Banach-Stone theorem asserts that
unital commutative $C^*$-algebras are isometric as Banach spaces if and on
ly if they are isomorphic as Banach algebras.\n\nProblem: For which (commu
tative) Banach algebras does the Banach space structures ensure the Banach
algebra structure?\n\nA theorem of Nagasawa (1959)\, or deLeeuw\, Rudin a
nd Wermer (1960) states that a surjective complex-linear isometry between
uniform algebras is a weighted composition operator. Hence a uniform algeb
ra satisfies the mentioned property in Problem. A standard proof of the th
eorem depends on the so-called extreme point argument. The Arens-Kelley th
eorem asserts that an extreme point of the closed unit ball of the dual sp
ace of a uniform algebra is the point evaluation at a Choquet boundary poi
nt followed by a scalar multiplication of the unit modulus. Thus the dual
map of the given isometry gives the correspondence between the Choquet bou
ndaries\, which induces the composition part of the isometry. It is intere
sting that\nthe first result on isometries of the Hardy spaces depend on t
his theorem.\nOn the other hand\, the dual space of the Wiener algebra $W(
{\\mathbb T})=\\{f\\in C({\\mathbb T}):\\sum|\\hat{f}(n)|<\\infty\\}$ is $
\\ell^\\infty({\\mathbb Z})$\, and an Arens-Kelley theorem does not hold f
or the Wiener algebra. For any bijection $\\varphi$ from the set of the po
sitive integers onto the set of all integers\, the map $T:W({\\mathbb T})\
\to W_+({\\mathbb T})$ defined by\n\\[\nT(f)(e^{i\\theta})=\\sum_{n=0}^\\i
nfty \\hat{f}(\\varphi(n))e^{in\\theta}\,\\quad f\\in W({\\mathbb T})\n\\]
\nis a surjective complex-linear isometry\, where\n$W_+({\\mathbb T})=\\{f
\\in W({\\mathbb T}):\\hat{f}(n)=0\, \\forall n<0\\}$ is a closed subalgeb
ra of $W({\\mathbb T})$. On the other hand\, $W({\\mathbb T})$ is not alge
braically isomorphic as Banach algebra to $W_+({\\mathbb T})$ since the ma
ximal ideal spaces of these two algebras are not homeomorphic to each othe
r.\nThis reminds us that the class of Banach algebras which satisfy the me
ntioned property in Problem \nis not so large. The answer to Problem is f
ar from being completed.\n\nI will give a survey talk concerning to Proble
m and the related subjects such as isometries on spaces of analytic functi
ons.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marten Wortel (University of Pretoria)
DTSTART:20200812T110000Z
DTEND:20200812T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/12
DESCRIPTION:Title: Order isomorphisms between effect algebras of atomic JBW-
algebras\nby Marten Wortel (University of Pretoria) as part of Preserv
er Webinar\n\n\nAbstract\nIn this talk we will discuss an extension of a r
ecent paper by Semrl that characterised order isomorphisms of the effect a
lgebra (the self-adjoint operators on a Hilbert space between the zero and
identity operator) to atomic JBW-algebras. The first part of the talk wil
l be devoted to giving a brief introduction to Jordan operator algebras\,
focussing on the motivations why one would want to consider the more gener
al but slightly more complicated Jordan setting instead of just the operat
or algebra setting. In the second part of the talk we will explain the ide
as behind our proof for the atomic JBW-algebra case.\n\nThis is joint work
with Mark Roelands.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timur Oikhberg (University of Illinois)
DTSTART:20200819T140000Z
DTEND:20200819T150000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/13
DESCRIPTION:Title: Stability of disjointness preservation\nby Timur Oikh
berg (University of Illinois) as part of Preserver Webinar\n\n\nAbstract\n
An operator $T$ between Banach lattices $E$ and $F$ is said to be $\\varep
silon$-disjointness preserving ($\\varepsilon$-DP for short) if we have $\
\| |Tx| \\wedge |Ty| \\| \\leq \\varepsilon$ whenever $x$ and $y$ are disj
oint elements of $E$. $0$-DP operators are simply called disjointness pres
erving\, or DP for short. One can easily show that\, if $T$ is DP\, then $
S$ is $3\\|T-S\\|$-DP. We are interested in the converse of this statement
: if $T$ is $\\varepsilon$-DP\, must it be a small perturbation of a DP op
erator? In many cases\, the answer is positive\; however\, some counterexa
mples also exist.\n\nWe also consider stability of some related properties
for Banach lattices\, as well as similar questions in the non-commutative
setting.\n\nThis is a joint work with P.Tradacete.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ngai-Ching Wong (National Sun Yat-sen University)
DTSTART:20200826T110000Z
DTEND:20200826T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/14
DESCRIPTION:Title: Disjointness preservers of operator algebras\nby Ngai
-Ching Wong (National Sun Yat-sen University) as part of Preserver Webinar
\n\n\nAbstract\nI will report my 25 year struggle with the problem of whet
her a linear disjointness preserver\n$T$ between two C*-algebras $A$ and $
B$ is close to an algebra/Jordan (*-)homomorphism. \nHere\, the disjointne
ss of two elements $a\, b$ in a C*-algebra can have at least 5 versions\;
namely\,\n\n$$ab = 0\, a^*b=0\, ab^*=0\, a^*b=ab^*=0\, \\text{ or } ab=ba=
0.$$\n\nWhen $a\,b$ are self-adjoint\, all reduce to the zero product case
$ab=0$.\nFor example\, we ask what happens if $T$ preserves zero products
.\n\nWe attack the problem in several steps.\n\nIt is pretty fruitful when
$A\,B$ are commutative C*-algebras.\nIt is also satisfactory when $A\,B$
are matrix algebras.\nIn both cases\, a linear zero product preserver $T:
A\\to B$ is merely a direct sum\nof a good part $hJ$ and a `bad but small'
part.\nHere\, $h$ is a central element affiliated with $B$\, and $J$ is a
Jordan homomorphism.\nThe bad part arises either from the discontinuity\,
or the non-surjectivity of $T$ which\ntranslates into that the range $TA$
is not a C*-algebra.\n\nIn general\, we need to assume either the continu
ity or the surjectivity of $T$.\nWhen $T$ is a continuous linear disjointn
ess preserver\, we have a quite complete answer.\nIt merely says that $T=h
J$ is almost good.\n\nFor a surjective linear disjointness preserver $T: A
\\to B$\,\nwe have good answers for the cases when $A\,B$ are W*-algebras
or AW*-algebras.\nThe solutions are obtained by decomposing $T$ as a direc
t sum of surjective linear disjointness\npreservers between the abelian su
mmands and between the orthogonal complements. While the abelian\npart in
volves mainly topological arguments\, the nonabelian part relies on techni
ques dealing with projections.\n\nThe major obstruction to carry on to the
C*-algebra case is due to the lack\nof nontrivial projections for general
C*-algebras. We managed to finish the cases\nwhen $A\, B$ are type I or
properly infinite. \nFor a complete answer\, we devote a great efforts to
the developing of\ntwo type decomposition theories for general C*-algebras
\, so that any C*-algebra $A$ has\nan essential ideal which is a direct su
m of type A finite\, type A infinite\, type B finite\, type B infinite\,\n
and type C. Our plan is to solve the problem for surjective linear disjoi
ntness preservers between C*-algebras\nof each of these 5 types\, and `glu
e' the 5 versions together for a complete answer. \nUnfortunately\, we hav
e encountered big difficulties and struck for some years.\n\nWe have also
worked on other preserver problems for motivations\, \ne.g. linear orthogo
nality preservers of Hilbert C*-modules\, and orthogonal additive conforma
l disjointness preservers of C*-algebras.\n\nIn this talk\, I will present
some details of the above experience.\nThe above works are contributions
of many authors. Some of them are in the audience\, for example\,\nChi-Kw
ong Li\, Lajos Molnar and Antonio Peralta\, as well as some of my long tim
e collaborators\, \nChi-Wai Leung\, Lei Li\, Chi-Keung Ng\, Ming-Cheng Tsa
i and Ya-Shu Wang\, to name a few.\n\nI hope the audience can help to solv
e the problem.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haonan Zhang (IST Austria)
DTSTART:20200902T110000Z
DTEND:20200902T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/15
DESCRIPTION:Title: Data processing inequalities for alpha-z Rényi relative
entropies and the equality conditions\nby Haonan Zhang (IST Austria) a
s part of Preserver Webinar\n\n\nAbstract\nData processing inequality for
quantum relative entropy is a fundamental inequality in quantum informatio
n theory. The alpha-z Rényi relative entropies are a two-parameter family
of quantum Rényi relative entropies. In this talk we give the full range
of the parameters (alpha\,z) for which the data processing inequalities a
re valid and discuss their equality conditions. Along the way we review th
e results of joint convexity/concavity of certain trace functionals\, and
prove a conjecture of Audenaert and Datta and a conjecture of Carlen\, Fra
nk and Lieb.\n\nThe talk is based on two papers arXiv:1811.01205 and arXiv
:2007.06644.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Pankov (University of Warmia & Mazury\, Poland and Johannes K
epler Universität Linz\, Austria)
DTSTART:20200916T110000Z
DTEND:20200916T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/16
DESCRIPTION:Title: A geometric approach to Wigner-type theorems\nby Mark
Pankov (University of Warmia & Mazury\, Poland and Johannes Kepler Univer
sität Linz\, Austria) as part of Preserver Webinar\n\n\nAbstract\nLet $H$
be a complex Hilbert space and let ${\\mathcal P}(H)$ be the associated p
rojective space (the set of rank-one projections). Suppose that $\\dim H\\
ge 3$. We prove the following Wigner-type theorem: if $H$ is finite-dimens
ional\, then an arbitrary orthogonality preserving\ntransformation of ${\\
mathcal P}(H)$ (i.e. sending orthogonal projections to orthogonal projecti
ons\nwithout the assumption that the orthogonality relation is preserved i
n both directions) is induced by a unitary or anti-unitary operator. In th
e case when $H$ is infinite-dimensional\, this fails.\n\nThe problem is re
duced to a description of orthogonality preserving\nlineations. Lineations
are maps between projective spaces which send lines to\nsubsets of lines.
In general\, the behavior of lineations is complicated\;\nthey are not in
jective and can send lines to parts of lines only.\n\nOur version of Wigne
r's theorem is a consequence of the following\nresult:\nevery orthogonalit
y preserving lineation of ${\\mathcal P}(V)$ to itself\nis induced by\na l
inear or conjugate-linear isometry\n(now\, we do not require that $H$ is f
inite-dimensional).\n\nAs an application\, we describe (not necessarily i
njective)\ntransformations of Grassmannians preserving\nsome types of prin
cipal angles.\n\nThis is a joint work with Thomas Vetterlein.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dijana Ilisevic (University of Zagreb\, Croatia)
DTSTART:20200930T110000Z
DTEND:20200930T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/17
DESCRIPTION:Title: An inverse eigenvalue problem for isometries\nby Dija
na Ilisevic (University of Zagreb\, Croatia) as part of Preserver Webinar\
n\n\nAbstract\nThis talk is related to the following problem: when is a gi
ven finite set of modulus one complex numbers the spectrum of a linear iso
metry on a complex Banach space? Necessary conditions on such a set will b
e presented. Since sufficient conditions are related to the structure of s
pecific Banach spaces\, some particular cases will be considered and insig
htful examples will be given.\n\nThe core of this talk is based on the pap
er On isometries with finite spectrum\, written jointly with Fernanda Bote
lho\, accepted for publication in the Journal of Operator Theory.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miklós Pálfia (Sungkyunkwan University\, Republic of Korea)
DTSTART:20201021T110000Z
DTEND:20201021T120000Z
DTSTAMP:20260404T110827Z
UID:PreserverWebinar/18
DESCRIPTION:Title: Analytic lifts of operator monotone and concave functions
\nby Miklós Pálfia (Sungkyunkwan University\, Republic of Korea) as
part of Preserver Webinar\n\n\nAbstract\nIn the context of free function t
heory\, we review recent results on operator monotone and concave function
s in several variables. In particular we study the connection between oper
ator monotonicity and concavity on certain domains. It turns out\, that on
positive operators monotonicity and concavity are equivalent. Thus we exp
loit this to construct a non-commutative analytic lift for partially defin
ed functions such as multivariable real functions that are either operator
monotone or operator concave. These results can also be applied in more g
eneral settings\, like in the case of operator means of probability measur
es.\n\nWe will also study a version of monotonicity with respect to the re
al positive definite order introduced recently by Blecher. It turns out th
at the real parts of such functions are completely characterizable by oper
ator monotone functions. Moreover if the function is assumed to be free an
alytic\, then it must be affine linear. This latter part of the talk is ba
sed on a joint work with Marcell Gaál.\n
LOCATION:https://stable.researchseminars.org/talk/PreserverWebinar/18/
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