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ON n-IDEAL AMENABILITY OF CERTAIN BANACH ALGEBRAS

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  08 December 2011

ZEINAB KAMALI  and
MEHDI NEMATI
ZEINAB KAMALI*
Affiliation:
Department of Mathematical Sciences, Islamic Azad University, Khorasgan branch, Isfahan, Iran (email: [email protected])
MEHDI NEMATI
Affiliation:
Department of Mathematics, Faculty of Science, University of Kashan, Kashan 87317-51167, Iran (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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In this paper we consider some notions of amenability such as ideal amenability, n-ideal amenability and approximate n-ideal amenability. The first two were introduced and studied by Gordji, Yazdanpanah and Memarbashi. We investigate some properties of certain Banach algebras in each of these classes. Results are also given for Segal algebras on locally compact groups.

Keywords

Banach algebran-ideal amenabilityabstract Segal algebra

MSC classification

Secondary: 46H05: General theory of topological algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 1 , August 2012 , pp. 90 - 99
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Alaghmandan, M., Nasr-Isfahani, R. and Nemati, M., ‘Character amenability and contractibility of abstract Segal algebras’, Bull. Aust. Math. Soc. 82 (2010), 274–281.CrossRefGoogle Scholar
[2]Bade, W. G., Curtis, P. C. and Dales, H. G., ‘Amenability and weak amenability for Beurling and Lipschitz algebras’, Proc. Lond. Math. Soc. 55 (1987), 359–377.CrossRefGoogle Scholar
[3]Dales, H. G., Banach Algebras and Automatic Continuity (Clarendon Press, Oxford, 2000).Google Scholar
[4]Dales, H. G., Ghahramani, F. and Grønbæk, N., ‘Derivations into iterated duals of Banach algebras’, Studia Math. 128 (1998), 19–53.Google Scholar
[5]Eshaghi Gordji, M. and Memarbashi, R., ‘Derivations into nth duals of ideals of Banach algebras’, Bull. Iran Math. Soc. 34 (2008), 59–71.Google Scholar
[6]Eshaghi Gordji, M. and Yazdanpanah, T., ‘Derivations into duals of ideals of Banach algebras’, Proc. Indian Acad. Sci. 114 (2004), 399–408.Google Scholar
[7]Ghahramani, F. and Lau, A. T.-M., ‘Approximate weak amenability, derivations and Arens regularity of Segal algebras’, Studia Math. 169 (2005), 189–205.CrossRefGoogle Scholar
[8]Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis, Vol. I, Grundlehren der Mathematischen Wissenschaften, 152 (Springer, Berlin, 1970).Google Scholar
[9]Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis, 2nd edn, Vol. II, Grundlehren der Mathematischen Wissenschaften, 115 (Springer, Berlin, 1979).CrossRefGoogle Scholar
[10]Jabbari, A., Moslehian, M. S. and Vishki, H. R. E., ‘Constructions preserving n-weak amenability of Banach algebras’, Math. Bohem. 134 (2009), 349–357.CrossRefGoogle Scholar
[11]Johnson, B. E., ‘Derivations from L 1(G) into L 1(G) and L ∞(G)’, in: Proc. Internat. Conf. on Harmonic Analysis, Luxembourg 1987, Lecture Notes in Mathematics, 1359 (Springer, Berlin–New York, 1988), pp. 191–198.Google Scholar
[12]Kotzmann, E. and Rindler, H., ‘Segal algebras on non-abelian groups’, Trans. Amer. Math. Soc. 237 (1978), 271–281.CrossRefGoogle Scholar
[13]Lau, A. T.-M. and Loy, R. J., ‘Weak amenability of Banach algebras on locally compact groups’, J. Funct. Anal. 145 (1997), 175–204.CrossRefGoogle Scholar
[14]Leinert, M., ‘A contribution to Segal algebras’, Manuscripta Math. 10 (1973), 297–306.CrossRefGoogle Scholar
[15]Mewomo, O. T., ‘On approximate ideal amenability in Banach algebras’, Mathematică LVI (2010), 199–208.Google Scholar
[16]Reiter, H., L1-Algebras and Segal Algebras, Lecture Notes in Mathematics, 231 (Springer, Berlin, 1971).CrossRefGoogle Scholar
[17]Samea, H., ‘Approximate weak amenability of abstract Segal algebras’, Math. Scand 106 (2010), 243–249.CrossRefGoogle Scholar
[18]Zhang, Y., ‘Weak amenability of module extensions of Banach algebras’, Trans. Amer. Math. Soc. 354 (2010), 4131–4151.CrossRefGoogle Scholar