Hahn-Banach for metric functionals and horofunctions
Metric Geometry
2020-01-15 v1 Functional Analysis
Abstract
It is observed that a natural analog of the Hahn-Banach theorem is valid for metric functionals but fails for horofunctions. Several statements of the existence of invariant metric functionals for individual isometries and 1-Lipschitz maps are proved. Various other definitions, examples and facts are pointed out related to this topic. In particular it is shown that the metric (horofunction) boundary of every infinite Cayley graphs contains at least two points.
Cite
@article{arxiv.2001.04742,
title = {Hahn-Banach for metric functionals and horofunctions},
author = {Anders Karlsson},
journal= {arXiv preprint arXiv:2001.04742},
year = {2020}
}
Comments
15 pages, 3 figures