Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces
Résumé
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.
Domaines
Géométrie métrique [math.MG]| Origine | Fichiers produits par l'(les) auteur(s) |
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