The group $\Aut(μ)$ is Roelcke precompact
| dc.creator | Glasner, Eli | |
| dc.date | 2009-02-22 | |
| dc.date.accessioned | 2026-07-07T12:45:31Z | |
| dc.date.available | 2026-07-07T12:45:31Z | |
| dc.description | 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 $G= \Aut(μ)$, of automorphisms of an atomless standard Borel probability space $(X,μ)$, is precompact. We identify the corresponding compactification as the space of Markov operators on $L_2(μ)$ 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. | |
| dc.identifier | https://arxiv.org/abs/0902.3786 | |
| dc.identifier | http://arxiv.org/abs/0902.3786 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221109 | |
| dc.subject | Dynamical Systems | |
| dc.subject | General Topology | |
| dc.subject | 54H11, 22A05 (Primary) 37B05, 54H20 (Secondary) | |
| dc.title | The group $\Aut(μ)$ is Roelcke precompact | |
| dc.type | text |