Weakly amenable groups

TL;DR

This paper introduces the concept of weakly amenable groups, constructs the first examples of finitely generated non-amenable weakly amenable groups, and explores their properties.

Contribution

It defines weak amenability in groups and provides the first known finitely generated non-amenable examples, advancing understanding of group representations.

Findings

First finitely generated non-amenable weakly amenable groups constructed

Weak amenability characterized by the regular representation's relation to the trivial representation

New examples expand the class of groups studied in harmonic analysis

Abstract

In this paper, a group is called weakly amenable if its left regular representation is not uniformly isolated from the trivial representation. First examples of finitely generated non-amenable weakly amenable groups are constructed.