Structure of preservers of range orthogonality on *-rings and C*-algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00359334" target="_blank" >RIV/68407700:21230/22:00359334 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.laa.2022.02.025" target="_blank" >https://doi.org/10.1016/j.laa.2022.02.025</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.laa.2022.02.025" target="_blank" >10.1016/j.laa.2022.02.025</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Structure of preservers of range orthogonality on *-rings and C*-algebras

Popis výsledku v původním jazyce

The topic of this paper lies between algebraic theory of *-rings and *-algebras on one side, and analytic theory of C*-algebras on the other side. A map theta : A -> B between unital *-rings is called range orthogonal isomorphism if it is bijective and preserves range orthogonality in both directions. We show that any additive (resp. linear) range orthogonal isomorphism is canonical, that is, it is a *-isomorphism followed by multiplication from the right by an invertible element, provided that Ais generated by projections as a *-ring. In case of general * rings and *-algebras we show that direct summands generated by projections are well behaved with respect to range orthogonal morphisms. In particular, we show that additive range orthogonality isomorphisms are canonical on proper nonabelian parts of Baer *-algebras. We apply algebraic results to matrix C*-algebras to show that any range orthogonal isomorphisms between them is canonical. The same holds for C*-algebras having proper nonabelian part generated by projections. (C) 2022 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Structure of preservers of range orthogonality on *-rings and C*-algebras

Popis výsledku anglicky

The topic of this paper lies between algebraic theory of *-rings and *-algebras on one side, and analytic theory of C*-algebras on the other side. A map theta : A -> B between unital *-rings is called range orthogonal isomorphism if it is bijective and preserves range orthogonality in both directions. We show that any additive (resp. linear) range orthogonal isomorphism is canonical, that is, it is a *-isomorphism followed by multiplication from the right by an invertible element, provided that Ais generated by projections as a *-ring. In case of general * rings and *-algebras we show that direct summands generated by projections are well behaved with respect to range orthogonal morphisms. In particular, we show that additive range orthogonality isomorphisms are canonical on proper nonabelian parts of Baer *-algebras. We apply algebraic results to matrix C*-algebras to show that any range orthogonal isomorphisms between them is canonical. The same holds for C*-algebras having proper nonabelian part generated by projections. (C) 2022 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/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Centrum pokročilých aplikovaných přírodních věd</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Linear Algebra and Its Applications

ISSN

0024-3795

e-ISSN

1873-1856

Svazek periodika

642

Číslo periodika v rámci svazku

JUN

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

139-159

Kód UT WoS článku

000819927900008

EID výsledku v databázi Scopus

2-s2.0-85125449947