Examples of groups which are not weakly amenable

TL;DR

The paper investigates conditions under which locally compact groups are not weakly amenable, extending previous results and providing new insights into the structure of such groups and their von Neumann algebra counterparts.

Contribution

It establishes that weak amenability imposes strict conditions on amenable closed normal subgroups, extending earlier non-weak amenability results and including a von Neumann algebra analogue.

Findings

Weak amenability constrains the structure of amenable closed normal subgroups.

Extension of non-weak amenability results by Haagerup and Ozawa--Popa.

Provides a von Neumann algebra analogue of the main results.

Abstract

We prove that weak amenability of a locally compact group imposes a strong condition on its amenable closed normal subgroups. This extends non weak amenability results of Haagerup (1988) and Ozawa--Popa (2010). A von Neumann algebra analogue is also obtained.