On co-amenability for groups and von Neumann algebras

TL;DR

This paper investigates the property of co-amenability in groups and von Neumann algebras, revealing that co-amenability does not necessarily pass to subgroups and exploring its relationship with von Neumann algebras.

Contribution

It provides a counterexample to co-amenability passing to subgroups and clarifies the connection between co-amenability in groups and von Neumann algebras.

Findings

Co-amenability does not pass to subgroups.

Relationship between co-amenability in groups and von Neumann algebras clarified.

Addresses a question posed by Eymard in 1972.

Abstract

We first show that co-amenability does not pass to subgroups, answering a question asked by Eymard in 1972. We then address co-amenability for von Neumann algebras, describing notably how it relates to the former.