| Title:
|
On heredity of strongly proximal actions (English) |
| Author:
|
Raja, C. Robinson Edward |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
51-55 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that action of a semigroup $T$ on compact metric space $X$ by continuous selfmaps is strongly proximal if and only if $T$ action on ${\mathcal P}(X)$ is strongly proximal. As a consequence we prove that affine actions on certain compact convex subsets of finite-dimensional vector spaces are strongly proximal if and only if the action is proximal. (English) |
| Keyword:
|
proximal and strongly proximal actions |
| Keyword:
|
probability measures |
| MSC:
|
37A15 |
| MSC:
|
37B05 |
| MSC:
|
54H20 |
| MSC:
|
60B05 |
| idZBL:
|
Zbl 1110.37005 |
| idMR:
|
MR1982211 |
| . |
| Date available:
|
2008-06-06T22:41:14Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107853 |
| . |
| Reference:
|
[B] Billingley P.: Convergence of Probability Measures.John Willey and Sons, New York-Toronto, 1968. MR 0233396 |
| Reference:
|
[G] Glasner S.: Proximal flows on Lie groups.Israel Journal of Mathematics 45 (1983), 97–99. MR 0719114 |
| Reference:
|
[P] Parthasarathy K. R.: Probability Measures on Metric Spaces.Academic Press, New York-London, 1967. Zbl 0153.19101, MR 0226684 |
| . |
