Abstract
Let (G,X) be a transformationgroup where the groupG does not necessarily act freely on the space X. We investigate the extent to which the action of G may fail to be proper. Stability subgroups are used to define new notions of strength of convergence in the orbit space and of measure accumulation along orbits. By using the representation theory of the associated crossed product C¿-algebra, we show that these notions are equivalent under certain conditions.
| Original language | English |
|---|---|
| Pages (from-to) | 819-845 |
| Number of pages | 27 |
| Journal | Journal of Functional Analysis |
| Volume | 263 |
| Issue number | 4 |
| Early online date | 18 May 2012 |
| DOIs | |
| Publication status | Published - 15 Aug 2012 |
Keywords
- transformation group
- stability subgroup
- orbit space
- proper action
- k-Times convergence
- measure accumulation
- crossed-product C¿-algebra
- induced representation
- spectrum of a C¿-algebra
- multiplicity of a representation