Amenable semigroups and nonexpansive dynamical systems

2019/09/20 by Andrzej Wiśnicki, Wiśnicki, Andrzej
Computer Science · Mathematics · #Optimization and Variational Analysis #Advanced Banach Space Theory #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1909.09723

Abstract

We characterize amenability of subspaces of C(S), where S 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-Nikodým property, and in the duals of M-embedded Banach spaces.

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