| Title:
|
Module $(\varphi,\psi)$-amenability of Banach algebras (English) |
| Author:
|
Bodaghi, Abasalt |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
46 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
227-235 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $S$ be an inverse semigroup with the set of idempotents $E$ and $S/\approx$ be an appropriate group homomorphic image of $S$. In this paper we find a one-to-one correspondence between two cohomology groups of the group algebra $\ell ^1(S)$ and the semigroup algebra $ {\ell ^{1}}(S/\approx )$ with coefficients in the same space. As a consequence, we prove that $S$ is amenable if and only if $S/\approx $ is amenable. This could be considered as the same result of Duncan and Namioka [5] with another method which asserts that the inverse semigroup $S$ is amenable if and only if the group homomorphic image $S/\sim $ is amenable, where $\sim $ is a congruence relation on $S$. (English) |
| Keyword:
|
Banach modules |
| Keyword:
|
module derivation |
| Keyword:
|
module amenability |
| Keyword:
|
inverse semigroup |
| MSC:
|
43A07 |
| MSC:
|
46H25 |
| idZBL:
|
Zbl 1240.43001 |
| idMR:
|
MR2754062 |
| . |
| Date available:
|
2010-12-14T14:54:14Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141377 |
| . |
| Reference:
|
[1] Amini, M.: Module amenability for semigroup algebras.Semigroup Forum 69 (2004), 243–254. Zbl 1059.43001, MR 2081295, 10.1007/s00233-004-0107-3 |
| Reference:
|
[2] Amini, M., Bodaghi, A., Bagha, D. Ebrahimi: Module amenability of the second dual and module topological center of semigroup algebras.Semigroup Forum 80 (2010), 302–312. MR 2601766, 10.1007/s00233-010-9211-8 |
| Reference:
|
[3] Amioni, M.: Corrigendum, Module amenability for semigroup algebras.Semigroup Forum 72 (2006), 493. MR 2228544 |
| Reference:
|
[4] Dale, H. G.: Banach Algebra and Automatic Continuity.Oxford university Press, 2000. |
| Reference:
|
[5] Duncan, J., Namioka, I.: Amenability of inverse semigroups and their semigroup algebra.Proc. Roy. Soc. Edinburgh Sect. A 80 (3–4) (1978), 309–321. MR 0516230 |
| Reference:
|
[6] Howie, J. M.: An Introduction to Semigroup Theory.London Academic Press, 1976. Zbl 0355.20056, MR 0466355 |
| Reference:
|
[7] Johnson, B. E.: Cohomology in Banach algebras.Mem. Amer. Math. Soc. 127 (1972), iii+96 pp. Zbl 0256.18014, MR 0374934 |
| Reference:
|
[8] Moslehian, M. S., Motlagh, A. N.: Some notes on $(\sigma ,\tau )$-amenability of Banach algebras.Stud. Univ. Babeş-Bolyai Math. 53 (3) (2008), 57–68. Zbl 1199.46111, MR 2487108 |
| Reference:
|
[9] Munn, W. D.: A class of irreducible matrix representations of an arbitrary inverse semigroup.Proc. Glasgow Math. Assoc. 5 (1961), 41–48. Zbl 0113.02403, MR 0153762 |
| Reference:
|
[10] Paterson, A. L. T.: Groupoids, Inverse Semigroups, and Their Operator Algebras.Birkhäuser, Boston, 1999. Zbl 0913.22001, MR 1724106 |
| Reference:
|
[11] Rezavand, R., Amini, M., Sattari, M. H., Bagh, D. Ebrahimi: Module Arens regularity for semigroup algebras.Semigroup Forum 77 (2008), 300–305. MR 2443440, 10.1007/s00233-008-9075-3 |
| Reference:
|
[12] Wilde, C., Argabright, L.: Invariant means and factor semigroup.Proc. Amer. Math. Soc. 18 (1967), 226–228. MR 0215064, 10.1090/S0002-9939-1967-0215064-9 |
| . |
