Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces
Annales de l'Institut Fourier, Volume 68 (2018) no. 5, pp. 1831-1877.

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.

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.

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DOI: 10.5802/aif.3198
Classification: 46A40,  46B04,  46A55
Keywords: Hilbert metric, cone, isometry, Banach space, horofunction boundary
License: CC-BY-ND 4.0
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Walsh, Cormac. Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces. Annales de l'Institut Fourier, Volume 68 (2018) no. 5, pp. 1831-1877. doi : 10.5802/aif.3198. https://aif.centre-mersenne.org/articles/10.5802/aif.3198/

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