Approximate fixed points and B-amenable groups

TL;DR

This paper characterizes B-amenable groups via the existence of approximate fixed points for continuous affine actions on bounded convex sets, extending to semigroup actions.

Contribution

It provides a new characterization of B-amenability through approximate fixed points, generalizing previous results to semigroup actions.

Findings

B-amenability is equivalent to approximate fixed points for affine actions.

Results extend to slightly uniformly continuous semigroup actions.

Offers a new perspective on topological group properties.

Abstract

A topological group $G$ is B-amenable if and only if every continuous affine action of $G$ on a bounded convex subset of a locally convex space has an approximate fixed point. Similar results hold more generally for slightly uniformly continuous semigroup actions.