Group amenability properties for von Neumann algebras
Anthony LauAlan Paterson
22D1022D2543A07amenable representation$G$-amenability$G$-fixed point propertyHopf-von Neumann algebrasF\o lner conditions
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 $G$.
Indiana University Mathematics Journal
2006
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10.1512/iumj.2006.55.2787
10.1512/iumj.2006.55.2787
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Indiana Univ. Math. J. 55 (2006) 1363 - 1388
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