Piecewise *-homomorphisms and Jordan maps on C*-algebras and factor von Neumann algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F18%3A00323414" target="_blank" >RIV/68407700:21230/18:00323414 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jmaa.2017.12.056" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2017.12.056</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2017.12.056" target="_blank" >10.1016/j.jmaa.2017.12.056</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Piecewise *-homomorphisms and Jordan maps on C*-algebras and factor von Neumann algebras

Popis výsledku v původním jazyce

We investigate maps between C*-algebras that are well behaved with respect to mutually commuting elements. We contribute to the Mackey-Gleason problem by showing that any continuous bijection between self-adjoint parts of C*-algebras that preserves triple product (a, b) -> aba, and is linear on commutative subspaces, is already linear. This allows us to describe such maps as direct differences of linear Jordan isomorphisms. We shall show that any weak*-continuous bijection between positive invertible elements of von Neumann factors (of dimension at least 9) that preserves products of commuting elements in both directions is of the form a -> e(Psi(log a))theta(a(c)), where theta is a linear Jordan *-isomorphism, c nonzero real number and Psi is a hermitian continuous functional. In a similar way we describe the same type of bicontinuous maps between unitary groups of von Neumann factors. General form of the above mentioned maps on C*-algebras is also presented. (C) 2017 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Piecewise *-homomorphisms and Jordan maps on C*-algebras and factor von Neumann algebras

Popis výsledku anglicky

We investigate maps between C*-algebras that are well behaved with respect to mutually commuting elements. We contribute to the Mackey-Gleason problem by showing that any continuous bijection between self-adjoint parts of C*-algebras that preserves triple product (a, b) -> aba, and is linear on commutative subspaces, is already linear. This allows us to describe such maps as direct differences of linear Jordan isomorphisms. We shall show that any weak*-continuous bijection between positive invertible elements of von Neumann factors (of dimension at least 9) that preserves products of commuting elements in both directions is of the form a -> e(Psi(log a))theta(a(c)), where theta is a linear Jordan *-isomorphism, c nonzero real number and Psi is a hermitian continuous functional. In a similar way we describe the same type of bicontinuous maps between unitary groups of von Neumann factors. General form of the above mentioned maps on C*-algebras is also presented. (C) 2017 Elsevier Inc. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA17-00941S" target="_blank" >GA17-00941S: Topologické a geometrické vlastnosti Banachových prostorů a operátorových algeber II</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

1096-0813

Svazek periodika

462

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

18

Strana od-do

1014-1031

Kód UT WoS článku

000435065200058

EID výsledku v databázi Scopus

2-s2.0-85042873919