Title:
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Constructions preserving $n$-weak amenability of Banach algebras (English) |
Author:
|
Jabbari, A. |
Author:
|
Moslehian, M. S. |
Author:
|
Vishki, H. R. E. |
Language:
|
English |
Journal:
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Mathematica Bohemica |
ISSN:
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0862-7959 (print) |
ISSN:
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2464-7136 (online) |
Volume:
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134 |
Issue:
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4 |
Year:
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2009 |
Pages:
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349-357 |
Summary lang:
|
English |
. |
Category:
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math |
. |
Summary:
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A surjective bounded homomorphism fails to preserve $n$-weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras. (English) |
Keyword:
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weak amenability |
Keyword:
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$n$-weak amenability |
Keyword:
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derivation |
Keyword:
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second dual |
Keyword:
|
direct sum |
Keyword:
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Banach algebra |
Keyword:
|
Arens product |
MSC:
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46H20 |
MSC:
|
46H25 |
idZBL:
|
Zbl 1212.46067 |
idMR:
|
MR2597230 |
DOI:
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10.21136/MB.2009.140667 |
. |
Date available:
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2010-07-20T18:08:19Z |
Last updated:
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2020-07-29 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/140667 |
. |
Reference:
|
[1] Arens, A.: The adjoint of a bilinear operation.Proc. Amer. Math. Soc. 2 (1951), 839-848. Zbl 0044.32601, MR 0045941, 10.1090/S0002-9939-1951-0045941-1 |
Reference:
|
[2] Bade, W. G., Curtis, P. C., Dales, H. G.: Amenability and weak amenability for Beurling and Lipschitz algebras.Proc. London Math. Soc. 55 (1987), 359-377. Zbl 0634.46042, MR 0896225 |
Reference:
|
[3] Dales, H. G.: Banach Algebras and Automatic Continuity.London Math. Soc. Monographs Vol. 24, Clarendon Press, Oxford (2000). Zbl 0981.46043, MR 1816726 |
Reference:
|
[4] Dales, H. G., Ghahramani, F., Grønbæk, N.: Derivations into iterated duals of Banach algebras.Studia Math. 128 (1998), 19-54. MR 1489459 |
Reference:
|
[5] Dales, H. G., Lau, A. T.-M.: The second duals of Beurling algebras.Mem. Amer. Math. Soc. 177 (2005). Zbl 1075.43003, MR 2155972 |
Reference:
|
[6] Ghahramani, F., Laali, J.: Amenability and topological centres of the second duals of Banach algebras.Bull. Austral. Math. Soc. 65 (2002), 191-197. Zbl 1029.46116, MR 1898533, 10.1017/S0004972700020232 |
Reference:
|
[7] Gronbæk, N.: Amenability and weak amenability of tensor algebras and algebras of nuclear operators.J. Austral. Math. Soc. (Series A) 51 (1991), 483-488. MR 1125449, 10.1017/S1446788700034649 |
Reference:
|
[8] Gronbæk, N.: Weak and cyclic amenability for non-commutative Banach algebras.Proc. Edinburgh Math. Soc. 35 (1992), 315-328. MR 1169250 |
Reference:
|
[9] Helemskii, A. Ya.: The Homology of Banach and Topological Algebras.Kluwer, Dordrecht (1989). MR 1093462 |
Reference:
|
[10] Hewitt, E., Ross, K. A.: Abstract Harmonic Analysis.Vol. I, Springer, Berlin (1963); Vol. II, Springer, Berlin, 1970. Zbl 0837.43002, MR 0551496 |
Reference:
|
[11] Johnson, B. E.: Weak amenability of group algebras.Bull. London Math. Soc. 23 (1991), 281-284. Zbl 0757.43002, MR 1123339, 10.1112/blms/23.3.281 |
Reference:
|
[12] Leptin, H.: Sur l'algèbre de Fourier d'un groupe localement compact.C. R. Acad. Sci. Paris, Sér. A 266 (1968), 1180-1182. Zbl 0169.46501, MR 0239002 |
Reference:
|
[13] 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:
|
[14] Runde, V.: Lectures on Amenability.Lecture Notes in Mathematics Vol. 1774, Springer (2002). Zbl 0999.46022, MR 1874893, 10.1007/b82937 |
Reference:
|
[15] Zhang, Y.: Weak amenability of module extensions of Banach algebras.Trans. Amer. Math. Soc. 354 (2002), 4131-4151. Zbl 1008.46019, MR 1926868, 10.1090/S0002-9947-02-03039-8 |
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