Maps preserving products of commuting elements in von Neumann algebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00370644" target="_blank" >RIV/68407700:21230/23:00370644 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jmaa.2023.127044" target="_blank" >https://doi.org/10.1016/j.jmaa.2023.127044</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2023.127044" target="_blank" >10.1016/j.jmaa.2023.127044</a>
Alternative languages
Result language
angličtina
Original language name
Maps preserving products of commuting elements in von Neumann algebras
Original language description
A bijective map between specific structures in operator algebras is called a piecewise isomorphism if it preserves products of commuting elements in both directions. We shall show that any bicontinuous piecewise isomorphism between positive cones of invertible elements in von Neumann algebras or between unitary groups of von Neumann algebras can be described in terms of the following parameters: (i) Jordan *-isomorphism between given algebras (ii) one fixed central element in domain (or range) algebra (iii) a hermitian linear map from one algebra into the center of the other one. Especially, in case of factors any piecewise isomorphism between unitary groups is a Jordan *-isomorphism or Jordan *-isomorphism composed with inversion. This extends hitherto known results from von Neumann factors to general von Neumann algebras and brings new Jordan invariants of operator structures.(c) 2023 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
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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)<br>S - Specificky vyzkum na vysokych skolach
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Analysis and Applications
ISSN
0022-247X
e-ISSN
1096-0813
Volume of the periodical
523
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
18
Pages from-to
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UT code for WoS article
000931438200001
EID of the result in the Scopus database
2-s2.0-85147824894