Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
weak amenability; $n$-weak amenability; derivation; second dual; direct sum; Banach algebra; Arens product
weak amenability; $n$-weak amenability; derivation; second dual; direct sum; Banach algebra; Arens product
Summary:
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.
References:
[1] Arens, A.: The adjoint of a bilinear operation. Proc. Amer. Math. Soc. 2 (1951), 839-848. DOI 10.1090/S0002-9939-1951-0045941-1 | MR 0045941 | Zbl 0044.32601
[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. MR 0896225 | Zbl 0634.46042
[3] Dales, H. G.: Banach Algebras and Automatic Continuity. London Math. Soc. Monographs Vol. 24, Clarendon Press, Oxford (2000). MR 1816726 | Zbl 0981.46043
[4] Dales, H. G., Ghahramani, F., Grønbæk, N.: Derivations into iterated duals of Banach algebras. Studia Math. 128 (1998), 19-54. MR 1489459
[5] Dales, H. G., Lau, A. T.-M.: The second duals of Beurling algebras. Mem. Amer. Math. Soc. 177 (2005). MR 2155972 | Zbl 1075.43003
[6] Ghahramani, F., Laali, J.: Amenability and topological centres of the second duals of Banach algebras. Bull. Austral. Math. Soc. 65 (2002), 191-197. DOI 10.1017/S0004972700020232 | MR 1898533 | Zbl 1029.46116
[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. DOI 10.1017/S1446788700034649 | MR 1125449
[8] Gronbæk, N.: Weak and cyclic amenability for non-commutative Banach algebras. Proc. Edinburgh Math. Soc. 35 (1992), 315-328. MR 1169250
[9] Helemskii, A. Ya.: The Homology of Banach and Topological Algebras. Kluwer, Dordrecht (1989). MR 1093462
[10] Hewitt, E., Ross, K. A.: Abstract Harmonic Analysis. Vol. I, Springer, Berlin (1963); Vol. II, Springer, Berlin, 1970. MR 0551496 | Zbl 0837.43002
[11] Johnson, B. E.: Weak amenability of group algebras. Bull. London Math. Soc. 23 (1991), 281-284. DOI 10.1112/blms/23.3.281 | MR 1123339 | Zbl 0757.43002
[12] Leptin, H.: Sur l'algèbre de Fourier d'un groupe localement compact. C. R. Acad. Sci. Paris, Sér. A 266 (1968), 1180-1182. MR 0239002 | Zbl 0169.46501
[13] Lau, A. T.-M., Loy, R. J.: Weak amenability of Banach algebras on locally compact groups. J. Funct. Anal. 145 (1997), 175-204. DOI 10.1006/jfan.1996.3002 | MR 1442165 | Zbl 0890.46036
[14] Runde, V.: Lectures on Amenability. Lecture Notes in Mathematics Vol. 1774, Springer (2002). DOI 10.1007/b82937 | MR 1874893 | Zbl 0999.46022
[15] Zhang, Y.: Weak amenability of module extensions of Banach algebras. Trans. Amer. Math. Soc. 354 (2002), 4131-4151. DOI 10.1090/S0002-9947-02-03039-8 | MR 1926868 | Zbl 1008.46019
Search
Partner of
