Group amenability properties for von Neumann algebras

Details Group amenability properties for von Neumann algebras Group amenability properties for von Neumann algebras

2007-04-20

arxiv.org/abs/0704.2796v2

Indiana University Mathematics Journal 55(2006), 1363-1388

Mathematics

Operator Algebras

Scientific paper

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 $G$.

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