A strengthened Kadison’s transitivity theorem for unital JB∗-algebras with applications to the Mazur–Ulam property
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
A strengthened Kadison’s transitivity theorem for unital JB∗-algebras with applications to the Mazur–Ulam property
Original language description
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.
Czech name
—
Czech description
—
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
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Analysis and Mathematical Physics
ISSN
1664-2368
e-ISSN
1664-235X
Volume of the periodical
15
Issue of the periodical within the volume
4
Country of publishing house
CH - SWITZERLAND
Number of pages
46
Pages from-to
91
UT code for WoS article
001510492800001
EID of the result in the Scopus database
2-s2.0-105008279586