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Horofunction compactifications of symmetric cones under Finsler distances

Lemmens, Bas (2023) Horofunction compactifications of symmetric cones under Finsler distances. Annales Fennici Mathematici, 48 (2). pp. 729-756. ISSN 2737-0690. E-ISSN 2737-114X. (doi:10.54330/afm.141190) (KAR id:93105)

Abstract

In this paper we consider symmetric cones as symmetric spaces equipped with invariant Finsler distances, namely the Thompson distance and the Hilbert distance. We establish a correspondence between the horofunction compactification of a symmetric cone $A_+^\circ$ under these invariant Finsler distances and the horofunction compactification of the normed space in the tangent bundle. More precisely, for the Thompson distance on $A^\circ_+$ we show that the exponential map extends as a homeomorphism between the horofunction compactification of the normed space in the tangent bundle, which is a JB-algebra, and the horofunction compactification of $A_+^\circ$. We give a complete characteristation of the Thompson distance horofunctions and provide an explicit extension of the exponential map. Analogues results are established for the Hilbert distance on the projective cone $PA_+^\circ$. The analysis yields a geometric description of the horofunction compactifications of these spaces in terms of the facial structure of the closed unit ball of the dual norm of the norm in the tangent space.

Item Type: Article
DOI/Identification number: 10.54330/afm.141190
Additional information: For the purpose of open access, the author(s) has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising.
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)
Depositing User: Bas Lemmens
Date Deposited: 07 Feb 2022 15:09 UTC
Last Modified: 08 Feb 2024 14:39 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/93105 (The current URI for this page, for reference purposes)

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