$2m$-Weak amenability of group algebras

TL;DR

This paper proves that the group algebra of any locally compact group is $2m$-weakly amenable for all integers $m q 1$, using fixed point properties of semigroups.

Contribution

It establishes the $2m$-weak amenability of group algebras for all integers $m q 1$, extending previous results in the field.

Findings

Group algebra $L^1(G)$ is $2m$-weakly amenable for all $m q 1

Application of fixed point properties to prove amenability

Generalization to all locally compact groups

Abstract

A common fixed point property for semigroups is applied to show that the group algebra $L^1(G)$ of a locally compact group $G$ is $2m$-weakly amenable for each integer $m\geq 1$.