Connes-amenability of Fourier--Stieltjes algebras

TL;DR

This paper characterizes when the Fourier--Stieltjes algebra of a locally compact group is Connes-amenable, establishing a precise connection between algebraic properties and the group's structure.

Contribution

It proves that $B(G)$ is Connes-amenable if and only if the group $G$ is almost abelian, providing a complete characterization.

Findings

$B(G)$ is Connes-amenable iff $G$ is almost abelian

Characterizes Connes-amenability in terms of group structure

Links algebraic properties to group-theoretic conditions

Abstract

Let $G$ be a locally compact group, and let $B(G)$ denote its Fourier--Stieltjes algebra. We show that $B(G)$ is Connes-amenable if and only if $G$ is almost abelian.