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Hilbert and Thompson isometries on cones in JB-algebras

Lemmens, Bas, Roelands, Mark, Wortel, Marten (2019) Hilbert and Thompson isometries on cones in JB-algebras. Mathematische Zeitschrift, 292 (3-4). pp. 1511-1547. ISSN 0025-5874. (doi:10.1007/s00209-018-2144-8) (KAR id:57343)

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Abstract

Hilbert's and Thompson's metric spaces on the interior of cones in JB-algebras are important examples of symmetric Finsler spaces. In this paper we characterize the Hilbert's metric isometries on the interiors of cones in JBW-algebras, and the Thompson's metric isometries on the interiors of cones in JB-algebras. These characterizations generalize work by Bosche on the Hilbert and Thompson isometries on symmetric cones, and work by Hatori and Molnar on the Thompson isometries on the cone of positive self-adjoint elements in a unital C* -algebra. To obtain the results we develop a variety of new geometric and Jordan algebraic techniques.

Item Type: Article
DOI/Identification number: 10.1007/s00209-018-2144-8
Uncontrolled keywords: Hilbert’s metric, Thompson’s metric, Order unit spaces, JB-algebras, Isometries, Symmetric Banach–Finsler manifolds
Subjects: Q Science
Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Divisions: Central Services > Information Services
Central Services > Universities at Medway
Central Services > Research and Innovation Services
Depositing User: Bas Lemmens
Date Deposited: 20 Sep 2016 09:00 UTC
Last Modified: 16 Feb 2021 13:37 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/57343 (The current URI for this page, for reference purposes)
Lemmens, Bas: https://orcid.org/0000-0001-6713-7683
Roelands, Mark: https://orcid.org/0000-0002-8885-9156
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