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Journal Articles Annales de l'Institut Fourier Year : 2018

Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces

Cormac Walsh

Abstract

We study the horofunction boundaries of Hilbert and Thompson geome-tries, 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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hal-01249343 , version 1 (31-12-2015)

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Cormac Walsh. Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces. Annales de l'Institut Fourier, 2018, 68 (5), pp.1831-1877. ⟨hal-01249343⟩
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