Lemmens, Bas, Roelands, Mark (2015) Unique geodesics for Thompson's metric. Annales de l’Institut Fourier (Grenoble), 65 (1). pp. 315-348. E-ISSN 1777-5310. (doi:10.5802/aif.2932) (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:41203)
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. | |
Official URL: https://doi.org/10.5802/aif.2932 |
Abstract
In this paper a geometric characterization of the unique geodesics in Thompson's metric spaces is presented. This characterization is used to prove a variety of other geometric results. Firstly, it will be shown that there exists a unique Thompson's metric geodesic connecting x and y in the cone of positive self-adjoint elements in a unital C∗-algebra if, and only if, the spectrum of x−1/2yx−1/2 is contained in {1/β,β} for some β≥1. A similar result will be established for symmetric cones. Secondly, it will be shown that if C° is the interior of a finite-dimensional closed cone C, then the Thompson's metric space (C°,dC) can be quasi-isometrically embedded into a finite-dimensional normed space if, and only if, C is a polyhedral cone. Moreover, (C°,dC) is isometric to a finite-dimensional normed space if, and only if, C is a simplicial cone. It will also be shown that if C° is the interior of a strictly convex cone C with 3≤dim C≤∞, then every Thompson's metric isometry is projectively linear.
Item Type: | Article |
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DOI/Identification number: | 10.5802/aif.2932 |
Additional information: | Open Access |
Subjects: |
Q Science Q Science > QA Mathematics (inc Computing science) Q Science > QA Mathematics (inc Computing science) > QA440 Geometry |
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: | 29 May 2014 10:37 UTC |
Last Modified: | 17 Aug 2022 10:57 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/41203 (The current URI for this page, for reference purposes) |
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