%0 Journal Article
%T Some extremely amenable groups
%A Thierry Giordano
%A Vladimir Pestov
%J Mathematics
%D 2001
%I arXiv
%X A topological group $G$ is extremely amenable if every continuous action of $G$ on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of a Lebesgue space with a non-atomic measure is extremely amenable with the weak topology but not with the uniform one. Strengthening a de la Harpe's result, we show that a von Neumann algebra is approximately finite-dimensional if and only if its unitary group with the strong topology is the product of an extremely amenable group with a compact group.
%U http://arxiv.org/abs/math/0109138v3