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Can one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries?

Cueto-Avellaneda, Maria, Peralta, Antonio M. (2021) Can one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries? Linear and Multilinear Algebra, 70 (22). pp. 7702-7727. ISSN 1563-5139. (doi:10.1080/03081087.2021.2003745) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:100893)

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Official URL:
https://doi.org/10.1080/03081087.2021.2003745

Abstract

Let M and N be two unital JB∗-algebras and let U(M) and U(N) denote the sets of all unitaries in M and N, respectively. We prove that the following statements are equivalent:

A) M and N are isometrically isomorphic as (complex) Banach spaces;

B) M and N are isometrically isomorphic as real Banach spaces;

C) there exists a surjective isometry Δ:U(M)→U(N).

We actually establish a more general statement asserting that, under some mild extra conditions, for each surjective isometry Δ:U(M)→U(N), we can find a surjective real linear isometry Ψ:M→N which coincides with Δ on the subset eiMsa. If we assume that M and N are JBW∗-algebras, then every surjective isometry Δ:U(M)→U(N) admits a (unique) extension to a surjective real linear isometry from M onto N. This is an extension of the Hatori–Molnár theorem to the setting of JB∗-algebras.

Item Type: Article
DOI/Identification number: 10.1080/03081087.2021.2003745
Uncontrolled keywords: Algebra and Number Theory
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: Engineering and Physical Sciences Research Council (https://ror.org/0439y7842)
Ministerio de Ciencia e Innovación (https://ror.org/05r0vyz12)
SWORD Depositor: JISC Publications Router
Depositing User: JISC Publications Router
Date Deposited: 14 Apr 2023 13:20 UTC
Last Modified: 17 Apr 2023 11:21 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/100893 (The current URI for this page, for reference purposes)

University of Kent Author Information

Cueto-Avellaneda, Maria.

Creator's ORCID: https://orcid.org/0000-0002-1208-5684
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