Spatial and non-spatial actions of Polish groups

被引:21
作者
Glasner, E [1 ]
Weiss, B
机构
[1] Tel Aviv Univ, Dept Math, Ramat Aviv, Israel
[2] Hebrew Univ Jerusalem, Inst Math, IL-91904 Jerusalem, Israel
关键词
D O I
10.1017/S0143385705000052
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 Levy group are whirly. We also show that in the Polish group Aut (X, X, mu), for the generic automorphism T the action of the subgroup A(T) = cls {T-n : n is an element of Z} on the Lebesgue space (X, X, mu) is whirly.
引用
收藏
页码:1521 / 1538
页数:18
相关论文
共 18 条
[1]  
[Anonymous], LECT NOTES MATH
[2]  
[Anonymous], ILLINOIS J MATH
[3]  
[Anonymous], 1976, LECT NOTES MATH
[4]  
Becker H., 1996, LONDON MATH SOC LECT, V232
[5]  
Danilenko Alexandre I., 2000, MAT FIZ ANAL GEOM, V7, P35
[6]  
Furstenberg H., 1981, RECURRENCE ERGODIC T
[7]   On minimal actions of Polish groups [J].
Glasner, E .
TOPOLOGY AND ITS APPLICATIONS, 1998, 85 (1-3) :119-125
[8]  
GLASNER E, IN PRESS ISRAEL J MA
[9]  
GLASNER E, 2003, SURVEYS MONOGR AM MA, V101
[10]   A TOPOLOGICAL APPLICATION OF THE ISOPERIMETRIC INEQUALITY [J].
GROMOV, M ;
MILMAN, VD .
AMERICAN JOURNAL OF MATHEMATICS, 1983, 105 (04) :843-854