Hilbert and thompson geometries isometric to infinite-dimensional banach spaces

Cormac Walsh

doi:10.5802/aif.3198

Hilbert and thompson geometries isometric to infinite-dimensional banach spaces

Cormac Walsh

Université Paris-Saclay

Research output: Contribution to journal › Article › peer-review

Abstract

We study the horofunction boundaries of Hilbert and Thompson geometries, and of Banach spaces, in arbitrary dimension. By comparing the boundaries of these spaces, we show that the only Hilbert and Thompson geometries that are isometric to Banach spaces are the ones defined on the cone of positive continuous functions on a compact space.

Original language	English
Pages (from-to)	1831-1877
Number of pages	47
Journal	Annales de l'Institut Fourier
Volume	68
Issue number	5
DOIs	https://doi.org/10.5802/aif.3198
Publication status	Published - 1 Jan 2018
Externally published	Yes

Keywords

Banach space
Cone
Hilbert metric
Horofunction boundary
Isometry

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10.5802/aif.3198

Cite this

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abstract = "We study the horofunction boundaries of Hilbert and Thompson geometries, and of Banach spaces, in arbitrary dimension. By comparing the boundaries of these spaces, we show that the only Hilbert and Thompson geometries that are isometric to Banach spaces are the ones defined on the cone of positive continuous functions on a compact space.",

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AB - We study the horofunction boundaries of Hilbert and Thompson geometries, and of Banach spaces, in arbitrary dimension. By comparing the boundaries of these spaces, we show that the only Hilbert and Thompson geometries that are isometric to Banach spaces are the ones defined on the cone of positive continuous functions on a compact space.

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KW - Cone

KW - Hilbert metric

KW - Horofunction boundary

KW - Isometry

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Hilbert and thompson geometries isometric to infinite-dimensional banach spaces

Abstract

Keywords

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