Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces
Metric Geometry
2016-10-25 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1610.07508,
title = {Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces},
author = {Cormac Walsh},
journal= {arXiv preprint arXiv:1610.07508},
year = {2016}
}
Comments
34 pages, 2 figures