Structure of preservers of range orthogonality on *-rings and C*-algebras
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Structure of preservers of range orthogonality on *-rings and C*-algebras
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Linear Algebra and Its Applications
ISSN
0024-3795
e-ISSN
1873-1856
Volume of the periodical
642
Issue of the periodical within the volume
JUN
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
139-159
UT code for WoS article
000819927900008
EID of the result in the Scopus database
2-s2.0-85125449947