A strengthened Kadison’s transitivity theorem for unital JB∗-algebras with applications to the Mazur–Ulam property

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10512345" target="_blank" >RIV/00216208:11320/25:10512345 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=KPJshU-raN" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=KPJshU-raN</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s13324-025-01068-4" target="_blank" >10.1007/s13324-025-01068-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A strengthened Kadison’s transitivity theorem for unital JB∗-algebras with applications to the Mazur–Ulam property

Popis výsledku v původním jazyce

The principal result in this note is a strengthened version of Kadison’s transitivity theorem for unital JB∗-algebras, showing that for each minimal tripotent e in the bidual, A∗∗, of a unital JB∗-algebra A, there exists a self-adjoint element h in A satisfying e≤exp(ih), that is, e is bounded by a unitary in the principal connected component of the unitary elements in A. This new result opens the way to attack new geometric results, for example, a Russo–Dye type theorem for maximal norm closed proper faces of the closed unit ball of A asserting that each such face F of A coincides with the norm closed convex hull of the unitaries of A which lie in F. Another geometric property derived from our results proves that every surjective isometry from the unit sphere of a unital JB∗-algebra A onto the unit sphere of any other Banach space is affine on every maximal proper face. As a final application we show that every unital JB∗-algebra A satisfies the Mazur–Ulam property, that is, every surjective isometry from the unit sphere of A onto the unit sphere of any other Banach space Y admits an extension to a surjective real linear isometry from A onto Y. This extends a contribution by M. Mori and N. Ozawa who have proved the same result for unital C∗-algebras.

Název v anglickém jazyce

A strengthened Kadison’s transitivity theorem for unital JB∗-algebras with applications to the Mazur–Ulam property

Popis výsledku anglicky

The principal result in this note is a strengthened version of Kadison’s transitivity theorem for unital JB∗-algebras, showing that for each minimal tripotent e in the bidual, A∗∗, of a unital JB∗-algebra A, there exists a self-adjoint element h in A satisfying e≤exp(ih), that is, e is bounded by a unitary in the principal connected component of the unitary elements in A. This new result opens the way to attack new geometric results, for example, a Russo–Dye type theorem for maximal norm closed proper faces of the closed unit ball of A asserting that each such face F of A coincides with the norm closed convex hull of the unitaries of A which lie in F. Another geometric property derived from our results proves that every surjective isometry from the unit sphere of a unital JB∗-algebra A onto the unit sphere of any other Banach space is affine on every maximal proper face. As a final application we show that every unital JB∗-algebra A satisfies the Mazur–Ulam property, that is, every surjective isometry from the unit sphere of A onto the unit sphere of any other Banach space Y admits an extension to a surjective real linear isometry from A onto Y. This extends a contribution by M. Mori and N. Ozawa who have proved the same result for unital C∗-algebras.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Analysis and Mathematical Physics

ISSN

1664-2368

e-ISSN

1664-235X

Svazek periodika

15

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

46

Strana od-do

91

Kód UT WoS článku

001510492800001

EID výsledku v databázi Scopus

2-s2.0-105008279586