Preservation of Order and Orthogonality on Preduals of Jordan Algebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F24%3A00381381" target="_blank" >RIV/68407700:21230/24:00381381 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00025-024-02138-y" target="_blank" >https://doi.org/10.1007/s00025-024-02138-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-024-02138-y" target="_blank" >10.1007/s00025-024-02138-y</a>
Alternative languages
Result language
angličtina
Original language name
Preservation of Order and Orthogonality on Preduals of Jordan Algebras
Original language description
We study linear maps between preduals of JBW-algebras that preserve orthogonal decompositions of functionals. We generalize and strengthen results of Bunce and Wright (Pac J Math 158(2):265-272, 1993) obtained for von Neumann algebras by characterizing continuous orthogonally decomposable linear maps between preduals of JBW-algebras. In particular, we show that Banach space adjoint of such morphism phidocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Phi $$end{document} is typically of the form phi*(y)=c pi(y)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Phi <^>*(y)= cpi (y)$$end{document}, where c is a central positive element and pidocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$pi $$end{document} is a Jordan homomorphism. Further we show that the order topology on preduals of JBW-algebras equals to the norm topology. This allows to relax continuity in characterization of orthogonally decomposable isomorphisms and show that order and orthogonality relation in preduals are complete invariants of JBW-algebras.
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/GA23-04776S" target="_blank" >GA23-04776S: Interplay of algebraic, metric, geometric and topological structures on Banach spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Results in Mathematics
ISSN
1422-6383
e-ISSN
1420-9012
Volume of the periodical
79
Issue of the periodical within the volume
3
Country of publishing house
CH - SWITZERLAND
Number of pages
21
Pages from-to
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UT code for WoS article
001178225500004
EID of the result in the Scopus database
2-s2.0-85187100620