Preservation of Order and Orthogonality on Preduals of Jordan Algebras

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Preservation of Order and Orthogonality on Preduals of Jordan Algebras

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Preservation of Order and Orthogonality on Preduals of Jordan Algebras

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA23-04776S" target="_blank" >GA23-04776S: Interakce algebraických, metrických, geometrických a topologických struktur na Banachových prostorech</a><br>

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Results in Mathematics

ISSN

1422-6383

e-ISSN

1420-9012

Svazek periodika

79

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

21

Strana od-do

—

Kód UT WoS článku

001178225500004

EID výsledku v databázi Scopus

2-s2.0-85187100620