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- W1660843490 abstract "Following a similar result of Uspenskij on the unitary group of a separable Hilbert space we show that with respect to the lower (or Roelcke) uniform structure the Polish group $G= Aut(mu)$, of automorphisms of an atomless standard Borel probability space $(X,mu)$, is precompact. We identify the corresponding compactification as the space of Markov operators on $L_2(mu)$ and deduce that the algebra of right and left uniformly continuous functions, the algebra of weakly almost periodic functions, and the algebra of Hilbert functions on $G$, all coincide. Again following Uspenskij we also conclude that $G$ is totally minimal." @default.
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- W1660843490 date "2009-02-22" @default.
- W1660843490 modified "2023-09-27" @default.
- W1660843490 title "The group $Aut(mu)$ is Roelcke precompact" @default.
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