Amenable semigroups and nonexpansive dynamical systems
Functional Analysis
2019-09-24 v1 Dynamical Systems
Abstract
We characterize amenability of subspaces of , where is a semitopological semigroup, in terms of fixed point properties of nonexpansive actions. In particular, we give a complete characterization of a semitopological semigroup with a left invariant mean on WAP(S) that answers a question of A.T.-M. Lau and Y. Zhang in the affirmative. We also propose a new approach to Lau's problem concerning a counterpart of Day-Mitchell's characterization of amenable semigroups and show some partial results, in the case of weak compact convex sets with the Radon-Nikod\'{y}m property, and in the duals of -embedded Banach spaces.
Cite
@article{arxiv.1909.09723,
title = {Amenable semigroups and nonexpansive dynamical systems},
author = {Andrzej Wiśnicki},
journal= {arXiv preprint arXiv:1909.09723},
year = {2019}
}