Title: Group amenability properties for von Neumann algebras

Authors: Alan Paterson and Anthony T. Lau

Issue: Volume 55 (2006), Issue 4, 1363-1388

Abstract: In his study of amenable unitary representations, M.E.B. Bekka asked if there is an analogue for such representations of the remarkable fixed-point property for amenable groups. In this paper, we prove such a fixed-point theorem in the more general context of a $G$-amenable von Neumann algebra $M$, where $G$ is a locally compact group acting on $M$. The F\o lner conditions of Connes and Bekka are extended to the case where $M$ is semifinite and admits a faithful, semifinite, normal trace which is invariant under the action of $G$.