This is an announcement for the paper “Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces” by Cormac Walshhttps://arxiv.org/find/math/1/au:+Walsh_C/0/1/0/all/0/1.

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.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1610.07508