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.
(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)

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. (Contact us about this Publication) | |

Official URL http://aif.cedram.org/aif-bin/item?id=AIF_2015__65... |

## 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^{?1/2}yx^{?1/2} is contained in {1/?,?} for some ??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?,d_C) can be quasi-isometrically embedded into a finite-dimensional normed space if, and only if, C is a polyhedral cone. Moreover, (C?,d_C) 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^o is the interior of a strictly convex cone C with 3?dimC<?, then every Thompson's metric isometry is projectively linear.

Item Type: | Article |
---|---|

Additional information: | Open Access |

Subjects: |
Q Science Q Science > QA Mathematics (inc Computing science) Q Science > QA Mathematics (inc Computing science) > QA440 Geometry |

Divisions: | Faculties > Sciences > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Bas Lemmens |

Date Deposited: | 29 May 2014 10:37 UTC |

Last Modified: | 17 Feb 2020 13:27 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/41203 (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 |

- Export to:
- RefWorks
- EPrints3 XML
- BibTeX
- CSV

- Depositors only (login required):