TY - JOUR
T1 - Spatial and non-spatial actions of Polish groups
AU - Glasner, E.
AU - Weiss, B.
PY - 2005/10
Y1 - 2005/10
N2 - For locally compact groups all actions on a standard measure algebra have a spatial realization. For many Polish groups this is no longer the case. However, we show here that for non-archimedean Polish groups all measure algebra actions do have spatial realizations. In the other direction we show that an action of a Polish group is whirly ('ergodic at the identity') if and only if it admits no spatial factors and that all actions of a Lévy group are whirly. We also show that in the Polish group Aut(X, X, μ), for the generic automorphism T the action of the subgroup Λ(T) = cls {Tn : n ∈ ℤ} on the Lebesgue space (X, X, μ) is whirly.
AB - For locally compact groups all actions on a standard measure algebra have a spatial realization. For many Polish groups this is no longer the case. However, we show here that for non-archimedean Polish groups all measure algebra actions do have spatial realizations. In the other direction we show that an action of a Polish group is whirly ('ergodic at the identity') if and only if it admits no spatial factors and that all actions of a Lévy group are whirly. We also show that in the Polish group Aut(X, X, μ), for the generic automorphism T the action of the subgroup Λ(T) = cls {Tn : n ∈ ℤ} on the Lebesgue space (X, X, μ) is whirly.
UR - http://www.scopus.com/inward/record.url?scp=33644620232&partnerID=8YFLogxK
U2 - 10.1017/S0143385705000052
DO - 10.1017/S0143385705000052
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:33644620232
SN - 0143-3857
VL - 25
SP - 1521
EP - 1538
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 5
ER -