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: | 04 Mar 2024 19:22 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/100893 (The current URI for this page, for reference purposes) |

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