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BEGIN:VEVENT
SUMMARY:Chi-Kwong Li (College of William and Mary\, Virginia)
DTSTART;VALUE=DATE-TIME:20200529T150000Z
DTEND;VALUE=DATE-TIME:20200529T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
UID:PreserverWebinar/1
DESCRIPTION:Title: Quantum states and quantum channels\nby Chi-Kwong Li (C
ollege of William and Mary\, Virginia) as part of Preserver Webinar\n\n\nA
bstract\nIn the Hilbert space formulation\, quantum states are density mat
rices\, i.e.\, positive semidefinite matrices with trace one\, and quantum
channels are trace preserving completely positive linear maps on matrices
. In this talk\, we will present some results on the existence of quantum
channels with some special properties. Open problems in constructing speci
al types of quantum channel will be mentioned.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lajos Molnár (University of Szeged)
DTSTART;VALUE=DATE-TIME:20200605T110000Z
DTEND;VALUE=DATE-TIME:20200605T120000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
UID:PreserverWebinar/2
DESCRIPTION:Title: Means and their preservers\nby Lajos Molnár (Universit
y of Szeged) as part of Preserver Webinar\n\n\nAbstract\nIn this talk we s
urvey our recent work on preservers related to operator means.\n\nWe deal
with morphisms with respect to means as operations on positive definite or
semidefinite cones in operator algebras and consider preservers of norms
of means in similar settings. The first group of questions are motivated b
y the study of certain isometries while the second group of problems have
a loose connection to quantum mechanical symmetry transformations. We disc
uss possibilities of transforming one mean to another one and\, if time pe
rmits\, we also present some characterizations of specific means.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Peralta (University of Granada)
DTSTART;VALUE=DATE-TIME:20200612T150000Z
DTEND;VALUE=DATE-TIME:20200612T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
UID:PreserverWebinar/3
DESCRIPTION:Title: Tingley's problem for subsets strictly smaller than the
unit sphere\nby Antonio Peralta (University of Granada) as part of Preser
ver Webinar\n\n\nAbstract\nThe celebrated Tingley's problem has focused th
e attention of a wide community of researchers on preservers in recent yea
rs. It admits the following easy statement: Suppose $\\Delta : S(X) \\to S
(Y)$ is a surjective isometry between the unit spheres of two Banach space
s $X$ and $Y$. Does $\\Delta$ admit an extension to a surjective linear is
ometry 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 answ
ers have produced a wide range of new tools and results with interesting g
eometric and analytic conclusion.\n\n\nThe reader might guess from the tit
le that we won't limit ourself to Tingley's problem in this talk. It is na
tural to challenge the audience to consider other variants. We shall deal
with one of the most attractive and we shall consider the posibility of ex
tending surjective isometries between proper subsets of the unit spheres (
for example\, the subset of extreme points of the closed unit ball\, the s
ubset 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 i
n a unital JB$^*$-algebra\, etcetera). We shall see that negative and posi
tive answers can be obtained.\n\n\n[1] M. Cueto-Avellaneda\, A.M. Peralta\
, The Mazur--Ulam property for commutative von Neumann algebras\, Linear a
nd Multilinear Algebra\, 68\, No. 2\, 337--362 (2020).\n\n \n[2] M. Cue
to-Avellaneda\, A.M. Peralta\, Can one identify two unital JB$^*$-algebras
by the metric spaces determined by their sets of unitaries?\, preprint 20
20\, arXiv:2005.04794\n\n[3] O. Hatori\, L. Molnar\, Isometries of the uni
tary groups and Thompson isometries of the spaces of invertible positive e
lements in C*-algebras\, J. Math. Anal. Appl.\, 409\, 158-167 (2014).\n\n[
4] G. Nagy\, Isometries of spaces of normalized positive operators under t
he 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\, Char
acterizing 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 un
it sphere of positive operators\, Banach J. Math. Anal.\, 13\, no. 1\, 91-
112 (2019).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matej Bresar (University of Ljubljana and University of Maribor)
DTSTART;VALUE=DATE-TIME:20200617T110000Z
DTEND;VALUE=DATE-TIME:20200617T120000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
UID:PreserverWebinar/4
DESCRIPTION:Title: Zero product determined algebras and commutativity pres
ervers\nby Matej Bresar (University of Ljubljana and University of Maribor
) as part of Preserver Webinar\n\n\nAbstract\nA (not necessarily associati
ve) 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 th
at $ab = 0$ implies $f(a\, b) = 0$ is of the form $f(a\, b) = \\varphi(ab
)$ for some\nlinear functional $\\varphi$ on $A$.\n\nIn the context of\nBa
nach algebras\, one adds the assumption that $f$ and $\\varphi$ are conti
nuous. We will first survey the general theory of zero product determined
algebras\, and then discuss its applications to commutativity preserving
linear maps.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michiya Mori (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20200624T110000Z
DTEND;VALUE=DATE-TIME:20200624T120000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
UID:PreserverWebinar/5
DESCRIPTION:Title: Lattice isomorphisms between projection lattices of von
Neumann algebras\nby Michiya Mori (University of Tokyo) as part of Preser
ver Webinar\n\n\nAbstract\nA von Neumann algebra is a weak operator closed
*-subalgebra of B(H)\,\nwhose study was initiated by Murray and von Neuma
nn in 1930’s. The\ncollection of projections of a von Neumann algebra fo
rms a lattice\, and\nits geometry has played a very important role in unde
rstanding the\nstructure of von Neumann algebras for more than 80 years.\n
\n\nIn this talk\, we consider the following fundamental question: What is
\nthe general form of lattice isomorphisms between projection lattices of\
nvon Neumann algebras? Von Neumann gave an answer to this question for\nty
pe $\\mathrm{II}_1$ factors. He proved that a lattice isomorphism can be d
escribed\nby means of a ring isomorphism between the algebras of affiliate
d\noperators. However\, apparently no answer to this question has been giv
en\nfor the general case (in particular for type $\\mathrm{III}$ von Neuma
nn algebras)\nuntil now. In this talk\, we begin with a brief recap of the
classical\ntheory of von Neumann algebras\, and then give an answer to ou
r question\nfor general von Neumann algebras (save type $\\mathrm{I}_1$ an
d $\\mathrm{I}_2$) using ring\nisomorphisms between the algebras of locall
y measurable operators. We\nalso consider a better description of ring iso
morphisms between locally\nmeasurable operator algebras\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Semrl (University of Ljubljana)
DTSTART;VALUE=DATE-TIME:20200701T110000Z
DTEND;VALUE=DATE-TIME:20200701T120000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
UID:PreserverWebinar/6
DESCRIPTION:Title: Loewner's theorem for maps on operator domains\nby Pete
r Semrl (University of Ljubljana) as part of Preserver Webinar\n\n\nAbstra
ct\nThe classical Loewner's theorem states that operator monotone function
s on real intervals are described by holomorphic functions on the upper ha
lf-plane. We prove an analogue where real intervals are replaced by operat
or domains\, operator monotone functions by local order isomorphisms\, and
upper half-plane by the set of all bounded operators whose imaginary part
is a positive invertible operator. We will present several results on loc
al order isomorphisms and pay a special attention to the finite-dimensiona
l case. This is a report on a joint work with Michiya Mori.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bas Lemmens (University of Kent)
DTSTART;VALUE=DATE-TIME:20200708T110000Z
DTEND;VALUE=DATE-TIME:20200708T120000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
UID:PreserverWebinar/7
DESCRIPTION:Title: A metric version of a theorem by Poincaré\nby Bas Lemm
ens (University of Kent) as part of Preserver Webinar\n\n\nAbstract\nNumer
ous theorems in several complex variables are instances of results in metr
ic geometry. In this talk we shall see that a classic theorem due to Poin
care\, which says that there is no biholomorphic map from the polydisc ont
o 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 Poinca
re's theorem can be derived from a result for products of proper geodesic
metric spaces. In fact\, the main goal of the talk is to present a gener
al criterion\, in terms of certain asymptotic geometric properties of the
individual metric spaces\, that yields an obstruction for the existence of
an isometric embedding between product metric spaces.\n\nThe key concepts
from metric geometry involved are: the horofunction boundary of metric s
paces\, the Busemann points\, and the detour distance. These concepts can\
, and have been\, successfully used to analyse preserver problems involvin
g isometries.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denny H. Leung (National University of Singapore)
DTSTART;VALUE=DATE-TIME:20200715T110000Z
DTEND;VALUE=DATE-TIME:20200715T120000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
UID:PreserverWebinar/8
DESCRIPTION:Title: Nonlinear biseparating maps\nby Denny H. Leung (Nationa
l University of Singapore) as part of Preserver Webinar\n\n\nAbstract\nLet
$X\,Y$ be topological spaces and $E$\, $F$ be normed spaces. Suppose tha
t $A(X\,E)$ is a vector subspace of $C(X\,E)$ (space of $E$-valued continu
ous functions on $X$) and $A(Y\,F)$ is a subspace of $C(Y\,F)$.\nAn additi
ve 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 disj
ointness preserving.\nIn this talk\, I will propose a definition of ``bi
separating'' for general nonlinear mappings. \nThen we will proceed to ana
lyze the structure of biseparating maps acting on various types of functio
n 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
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javad Mashreghi (Laval University)
DTSTART;VALUE=DATE-TIME:20200722T150000Z
DTEND;VALUE=DATE-TIME:20200722T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
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 say
about $T$ if we assume that ``it preserves outer functions''? Another rel
ated question is to consider linear functionals $T: H^p \\to \\mathbb{C}$
(again\, no continuity assumption) and ask about those functionals whose k
ernels do not include any outer function. We study such questions via an a
bstract result which can be interpreted as the generalized Gleason--Kahane
--\\.Zelazko theorem for modules. In particular\, we see that continuity o
f endomorphisms and functionals is a part of the conclusion. We go further
and also discuss GKZ in other function spaces\, e.g.\, Bergman\, Dirichle
t\, Besov\, the little Bloch\, and VMOA and even generally in RKHS.\n\nThi
s is a joint work with T. Ransford.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ying-Fen Lin (Queens University Belfast)
DTSTART;VALUE=DATE-TIME:20200729T110000Z
DTEND;VALUE=DATE-TIME:20200729T120000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
UID:PreserverWebinar/10
DESCRIPTION:Title: Schur multipliers and positive extensions\nby Ying-Fen
Lin (Queens University Belfast) as part of Preserver Webinar\n\n\nAbstract
\nThe positive completion problem for a partially defined matrix asks when
the unspecified entries can be determined in such a way that the resultin
g fully defined matrix is positive semi-definite. The problem has attracte
d a considerable attention in the literature\, and had been studied using
combinatorial approaches\, until Paulsen\, Power and Smith observed in the
late 1980's that it is closely related to completely positive maps and op
erator systems. \n\nIn this talk\, after presenting an overview of the cla
ssical problem\, I will discuss an infinite dimensional and continuous set
ting\, where finite matrices are replaced by measurable Schur multipliers.
I will first introduce scalar-valued and operator-valued Schur multiplier
s and their partially defined versions\, and present a Grothendieck-type c
haracterisation of operator-valued Schur multipliers. Then I will talk abo
ut the positive extension problem of Schur multipliers and characterise it
s affirmative solution in terms of structures on an operator system associ
ated with the domain of the Schur multipliers.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osamu Hatori (Niigata University)
DTSTART;VALUE=DATE-TIME:20200805T110000Z
DTEND;VALUE=DATE-TIME:20200805T120000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
UID:PreserverWebinar/11
DESCRIPTION:Title: When does an isometry on a Banach algebra preserve the
multiplicative structure?\nby Osamu Hatori (Niigata University) as part of
Preserver Webinar\n\n\nAbstract\nThe Banach-Stone theorem asserts that un
ital commutative $C^*$-algebras are isometric as Banach spaces if and only
if they are isomorphic as Banach algebras.\n\nProblem: For which (commuta
tive) Banach algebras does the Banach space structures ensure the Banach a
lgebra structure?\n\nA theorem of Nagasawa (1959)\, or deLeeuw\, Rudin and
Wermer (1960) states that a surjective complex-linear isometry between un
iform algebras is a weighted composition operator. Hence a uniform algebra
satisfies the mentioned property in Problem. A standard proof of the theo
rem depends on the so-called extreme point argument. The Arens-Kelley theo
rem asserts that an extreme point of the closed unit ball of the dual spac
e of a uniform algebra is the point evaluation at a Choquet boundary point
followed by a scalar multiplication of the unit modulus. Thus the dual ma
p of the given isometry gives the correspondence between the Choquet bound
aries\, which induces the composition part of the isometry. It is interest
ing that\nthe first result on isometries of the Hardy spaces depend on thi
s 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 for
the Wiener algebra. For any bijection $\\varphi$ from the set of the posi
tive integers onto the set of all integers\, the map $T:W({\\mathbb T})\\t
o W_+({\\mathbb T})$ defined by\n\\[\nT(f)(e^{i\\theta})=\\sum_{n=0}^\\inf
ty \\hat{f}(\\varphi(n))e^{in\\theta}\,\\quad f\\in W({\\mathbb T})\n\\]\n
is 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 subalgebra
of $W({\\mathbb T})$. On the other hand\, $W({\\mathbb T})$ is not algebr
aically isomorphic as Banach algebra to $W_+({\\mathbb T})$ since the maxi
mal ideal spaces of these two algebras are not homeomorphic to each other.
\nThis reminds us that the class of Banach algebras which satisfy the ment
ioned property in Problem \nis not so large. The answer to Problem is far
from being completed.\n\nI will give a survey talk concerning to Problem
and the related subjects such as isometries on spaces of analytic function
s.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marten Wortel (University of Pretoria)
DTSTART;VALUE=DATE-TIME:20200812T110000Z
DTEND;VALUE=DATE-TIME:20200812T120000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
UID:PreserverWebinar/12
DESCRIPTION:Title: Order isomorphisms between effect algebras of atomic JB
W-algebras\nby Marten Wortel (University of Pretoria) as part of Preserver
Webinar\n\nInteractive livestream: https://us02web.zoom.us/j/81714923522\
n\nAbstract\nIn this talk we will discuss an extension of a recent paper b
y Semrl that characterised order isomorphisms of the effect algebra (the s
elf-adjoint operators on a Hilbert space between the zero and identity ope
rator) to atomic JBW-algebras. The first part of the talk will be devoted
to giving a brief introduction to Jordan operator algebras\, focussing on
the motivations why one would want to consider the more general but slight
ly more complicated Jordan setting instead of just the operator algebra se
tting. In the second part of the talk we will explain the ideas behind our
proof for the atomic JBW-algebra case.\n\nThis is joint work with Mark Ro
elands.\n
URL:https://us02web.zoom.us/j/81714923522
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timur Oikhberg (University of Illinois)
DTSTART;VALUE=DATE-TIME:20200819T140000Z
DTEND;VALUE=DATE-TIME:20200819T150000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
UID:PreserverWebinar/13
DESCRIPTION:Title: Stability of disjointness preservation\nby Timur Oikhbe
rg (University of Illinois) as part of Preserver Webinar\n\nInteractive li
vestream: https://us02web.zoom.us/j/85003589244\n\nAbstract\nAn operator $
T$ between Banach lattices $E$ and $F$ is said to be $\\varepsilon$-disjoi
ntness preserving ($\\varepsilon$-DP for short) if we have $\\| |Tx| \\wed
ge |Ty| \\| \\leq \\varepsilon$ whenever $x$ and $y$ are disjoint elements
of $E$. $0$-DP operators are simply called disjointness preserving\, or D
P 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 operator? In ma
ny cases\, the answer is positive\; however\, some counterexamples also ex
ist.\n\nWe also consider stability of some related properties for Banach l
attices\, as well as similar questions in the non-commutative setting.\n\n
This is a joint work with P.Tradacete.\n
URL:https://us02web.zoom.us/j/85003589244
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ngai-Ching Wong (National Sun Yat-sen University)
DTSTART;VALUE=DATE-TIME:20200826T110000Z
DTEND;VALUE=DATE-TIME:20200826T120000Z
DTSTAMP;VALUE=DATE-TIME:20200812T031604Z
UID:PreserverWebinar/14
DESCRIPTION:Title: Disjointness preservers of operator algebras\nby Ngai-C
hing Wong (National Sun Yat-sen University) as part of Preserver Webinar\n
\nAbstract: TBA\n
END:VEVENT
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