Timeline for proper action and amenable action
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 12, 2012 at 19:37 | vote | accept | m07kl | ||
| Sep 3, 2011 at 22:19 | comment | added | Alain Valette | About the converse: if $G$ is amenable and infinite, the action of $G$ on a point is amenable but not proper. | |
| Sep 3, 2011 at 21:59 | comment | added | m07kl | This implies also that for a proper G-C*-algebra the reduced and full crossed products coincide by Theorem 5.3 in C. Anantharaman-Delaroche | |
| Sep 3, 2011 at 21:47 | comment | added | m07kl | OK, I see. For a locally compact paracompact Hausdorff space proper action is amenable. To see this if X is G-compact, then we can choose Bruhat function to be compactly supported. If X is not G-compact, Bruhat function comes from G-compact case by partition of unity since compact paracompact Hausdorff implies partition of unity. In this case Bruhat function is not compactly supported, but the intersection of support of Bruhat function with any G-compact set in X is compact. (We need also Usyhson's lemma to construct Bruhat function, but paracompact Hausdorff space is normal) | |
| Sep 3, 2011 at 20:53 | comment | added | m07kl | thanks a lot. Bruhat function exists if proper space X is also G-compact? what about converse? Is amenable action proper? | |
| Sep 3, 2011 at 18:18 | history | answered | Alain Valette | CC BY-SA 3.0 |