Nous étudions les frontières d’horofonctions des géométries de Hilbert et de Thompson, et des espaces de Banach, en dimension arbitraire. En comparant les frontières de ces espaces, nous montrons que les seules géométries de Hilbert et de Thompson qui sont isométriques à des espaces de Banach sont celles qui sont définies sur le cône de fonctions continues positives sur un espace compact.
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.
Révisé le : 2017-05-07
Accepté le : 2017-06-14
Publié le : 2018-11-22
Classification : 46A40, 46B04, 46A55
Mots clés : Hilbert metric, cone, isometry, Banach space, horofunction boundary
@article{AIF_2018__68_5_1831_0,
author = {Walsh, Cormac},
title = {Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces},
journal = {Annales de l'Institut Fourier},
pages = {1831--1877},
publisher = {Association des Annales de l'institut Fourier},
volume = {68},
number = {5},
year = {2018},
doi = {10.5802/aif.3198},
language = {en},
url = {archive.numdam.org/item/AIF_2018__68_5_1831_0/}
}
Walsh, Cormac. Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces. Annales de l'Institut Fourier, Tome 68 (2018) no. 5, pp. 1831-1877. doi : 10.5802/aif.3198. http://archive.numdam.org/item/AIF_2018__68_5_1831_0/
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