| Title:
|
A generalized notion of $n$-weak amenability (English) |
| Author:
|
Bodaghi, Abasalt |
| Author:
|
Shojaee, Behrouz |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
139 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
99-112 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the current work, a new notion of $n$-weak amenability of Banach algebras using homomorphisms, namely $(\varphi ,\psi )$-$n$-weak amenability is introduced. Among many other things, some relations between $(\varphi ,\psi )$-$n$-weak amenability of a Banach algebra $\mathcal {A}$ and $M_{m}(\mathcal {A})$, the Banach algebra of $m\times m$ matrices with entries from $\mathcal {A}$, are studied. Also, the relation of this new concept of amenability of a Banach algebra and its unitization is investigated. As an example, it is shown that the group algebra $L^1(G)$ is ($\varphi ,\psi $)-$n$-weakly amenable for any bounded homomorphisms $\varphi $ and $\psi $ on $L^1(G)$. (English) |
| Keyword:
|
Banach algebra |
| Keyword:
|
continuous homomorphism |
| Keyword:
|
$(\varphi ,\psi )$-derivation |
| Keyword:
|
$n$-weak amenability |
| MSC:
|
22D15 |
| MSC:
|
43A10 |
| MSC:
|
43A20 |
| MSC:
|
46H25 |
| idZBL:
|
Zbl 06362245 |
| idMR:
|
MR3231432 |
| DOI:
|
10.21136/MB.2014.143639 |
| . |
| Date available:
|
2014-03-20T08:32:33Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143639 |
| . |
| Reference:
|
[1] Bodaghi, A., Gordji, M. Eshaghi, Medghalchi, A. R.: A generalization of the weak amenability of Banach algebras.Banach J. Math. Anal. (electronic only) 3 (2009), 131-142. MR 2461753, 10.15352/bjma/1240336430 |
| Reference:
|
[2] Bonsall, F. F., Duncan, J.: Complete Normed Algebra.Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80 Springer, New York (1973). MR 0423029 |
| Reference:
|
[3] Choi, Y., Ghahramani, F., Zhang, Y.: Approximate and pseudo-amenability of various classes of Banach algebras.J. Funct. Anal. 256 (2009), 3158-3191. Zbl 1179.46040, MR 2504522, 10.1016/j.jfa.2009.02.012 |
| Reference:
|
[4] Dales, H. G., Ghahramani, F., Grønbæk, N.: Derivations into iterated duals of Banach algebras.Stud. Math. 128 (1998), 19-54. MR 1489459 |
| Reference:
|
[5] Gordji, M. Eshaghi, Jabbari, A.: Generalization of weak amenability of group algebras.arXiv:1303.4769v1. |
| Reference:
|
[6] Jabbari, A., Moslehian, M. S., Vishki, H. R. E.: Constructions preserving $n$-weak amenability of Banach algebras.Math. Bohem. 134 (2009), 349-357. Zbl 1212.46067, MR 2597230 |
| Reference:
|
[7] Johnson, B. E.: Cohomology in Banach Algebras.Mem. Am. Math. Soc. vol. 127 AMS, Providence, R.I. (1972). Zbl 0256.18014, MR 0374934 |
| Reference:
|
[8] Johnson, B. E.: Weak amenability of group algebras.Bull. Lond. Math. Soc. 23 (1991), 281-284. Zbl 0757.43002, MR 1123339, 10.1112/blms/23.3.281 |
| Reference:
|
[9] Lau, A. T.-M., Loy, R. J.: Weak amenability of Banach algebras on locally compact groups.J. Funct. Anal. 145 (1997), 175-204. Zbl 0890.46036, MR 1442165, 10.1006/jfan.1996.3002 |
| Reference:
|
[10] Losert, V.: The derivation problem for group algebras.Ann. Math. (2) 168 (2008), 221-246. Zbl 1171.43004, MR 2415402 |
| Reference:
|
[11] Mewomo, O. T., Akinbo, G.: A generalization of the $n$-weak amenability of Banach algebras.An. Ştiinţ. Univ. ``Ovidius'' Constanţa, Ser. Mat. 19 (2011), 211-222. Zbl 1224.46095, MR 2785698 |
| Reference:
|
[12] Moslehian, M. S., Motlagh, A. N.: Some notes on $(\sigma,\tau)$-amenability of Banach algebras.Stud. Univ. Babes-Bolyai Math. 53 (2008), 57-68. Zbl 1199.46111, MR 2487108 |
| Reference:
|
[13] Zhang, Y.: Weak amenability of a class of Banach algebras.Can. Math. Bull. 44 (2001), 504-508. Zbl 1156.46306, MR 1863642, 10.4153/CMB-2001-050-7 |
| . |
