| Title:
|
Uniqueness of means in the Cohen model (English) |
| Author:
|
Kalajdzievski, Damjan |
| Author:
|
Steprāns, Juris |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
60 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
49-60 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the question of whether or not an amenable subgroup of the permutation group on $\mathbb{N}$ can have a unique invariant mean on its action. We extend the work of M. Foreman (1994) and show that in the Cohen model such an amenable group with a unique invariant mean must fail to have slow growth rate and a certain weakened solvability condition. (English) |
| Keyword:
|
construction scheme |
| Keyword:
|
Knaster hierarchy |
| Keyword:
|
Cohen reals |
| MSC:
|
03E05 |
| MSC:
|
03E35 |
| MSC:
|
03E65 |
| idZBL:
|
Zbl 07088825 |
| idMR:
|
MR3946664 |
| DOI:
|
10.14712/1213-7243.2015.274 |
| . |
| Date available:
|
2019-05-13T07:46:22Z |
| Last updated:
|
2021-04-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147666 |
| . |
| Reference:
|
[1] Bartholdi L., Virág B.: Amenability via random walks.Duke Math. J. 130 (2005), no. 1, 39–56. MR 2176547, 10.1215/S0012-7094-05-13012-5 |
| Reference:
|
[2] Dushnik B., Miller E. W.: Partially ordered sets.Amer. J. Math. 63 (1941), no. 3, 600–610. MR 0004862, 10.2307/2371374 |
| Reference:
|
[3] Foreman M.: Amenable groups and invariant means.J. Funct. Anal. 126 (1994), no. 1, 7–25. MR 1305061, 10.1006/jfan.1994.1139 |
| Reference:
|
[4] Krasa S.: The action of a solvable group on an infinite set never has a unique invariant mean.Trans. Amer. Math. Soc. 305 (1988), no. 1, 369–376. MR 0920164, 10.1090/S0002-9947-1988-0920164-X |
| Reference:
|
[5] Paterson A. L. T.: Amenability.Mathematical Surveys and Monographs, 29, American Mathematical Society, Providence, 1988. Zbl 1106.22008, MR 0961261 |
| Reference:
|
[6] Rosenblatt J., Talagrand M.: Different types of invariant means.J. London Math. Soc. (2) 24 (1981), no. 3, 525–532. MR 0635883, 10.1112/jlms/s2-24.3.525 |
| Reference:
|
[7] Yang Z.: Action of amenable groups and uniqueness of invariant means.J. Funct. Anal. 97 (1991), no. 1, 50–63. MR 1105654, 10.1016/0022-1236(91)90015-W |
| . |
