Isomorphisms of ordered structures of abelian C*-subalgebras of C*-algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00182388" target="_blank" >RIV/68407700:21230/11:00182388 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jmaa.2011.05.035" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2011.05.035</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2011.05.035" target="_blank" >10.1016/j.jmaa.2011.05.035</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Isomorphisms of ordered structures of abelian C*-subalgebras of C*-algebras

Popis výsledku v původním jazyce

The aim of this note is to study the interplay between the Jordan structure of C*-algebra and the structure of its abelian C*-subalgebras. Let Abel(A) be a system of unital C*-subalgebras of a unital C*-algebra A ordered by set theoretic inclusion. We show that any order isomorphism phi : Abel(A) -> Abel(B) can be uniquely written in the form phi(C) = psi(C(sa)) + i psi (C(sa)), where psi is a partially linear Jordan isomorphism between self-adjoint parts of unital C*-algebras A and B. As a corollary weobtain that for certain class of C*-algebras (including von Neumann algebras) ordered structure of abelian subalgebras completely determines the Jordan structure. The results extend hitherto known results for abelian C*-algebras and may be relevant to foundations of quantum theory. (C) 2011 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Isomorphisms of ordered structures of abelian C*-subalgebras of C*-algebras

Popis výsledku anglicky

The aim of this note is to study the interplay between the Jordan structure of C*-algebra and the structure of its abelian C*-subalgebras. Let Abel(A) be a system of unital C*-subalgebras of a unital C*-algebra A ordered by set theoretic inclusion. We show that any order isomorphism phi : Abel(A) -> Abel(B) can be uniquely written in the form phi(C) = psi(C(sa)) + i psi (C(sa)), where psi is a partially linear Jordan isomorphism between self-adjoint parts of unital C*-algebras A and B. As a corollary weobtain that for certain class of C*-algebras (including von Neumann algebras) ordered structure of abelian subalgebras completely determines the Jordan structure. The results extend hitherto known results for abelian C*-algebras and may be relevant to foundations of quantum theory. (C) 2011 Elsevier Inc. All rights reserved.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Analysis and Its Applications

ISSN

0022-247X

e-ISSN

—

Svazek periodika

383

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

9

Strana od-do

391-399

Kód UT WoS článku

000292786100011

EID výsledku v databázi Scopus

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