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WEAK FORMS OF AMENABILITY FOR BANACH ALGEBRAS

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

Published online by Cambridge University Press:  30 November 2011

H. SAMEA
H. SAMEA*
Affiliation:
Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran (email: h.samea@basu.ac.ir)
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Abstract

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In this paper, the amenability and approximate amenability of weighted ℓp-direct sums of Banach algebras with unit, where 1≤p<∞, are completely characterized. Applications to compact groups and hypergroups are given.

Keywords

amenable Banach algebraapproximately amenable Banach algebracompact groupcompact hypergroup

MSC classification

Secondary: 46H20: Structure, classification of topological algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 3 , June 2012 , pp. 509 - 517
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Bharucha, P., Amenability properties and their consequences in Banach algebras, PhD Thesis, Australian National University, Australia, 2008.Google Scholar
[2]Bharucha, P. and Loy, R. J., ‘Approximate and weak amenability of certain Banach algebras’, Studia. Math. 197(2) (2010), 195–204.CrossRefGoogle Scholar
[3]Bloom, W. R. and Heyer, H., Harmonic Analysis of Probability Measures on Hypergroups (Walter de Gruyter, Berlin, 1995).CrossRefGoogle Scholar
[4]Bonsall, F. and Duncan, J., Complete Normed Algebras (Springer, New York, 1973).CrossRefGoogle Scholar
[5]Choi, Y. and Ghahramani, F., ‘Approximate amenability of Schatten classes, Lipschitz algebras and second duals of Fourier algebras’, Q. J. Math. 62(1) (2011), 39–58.CrossRefGoogle Scholar
[6]Dales, H. G., Loy, R. J. and Zhang, Y., ‘Approximate amenability for Banach sequence algebras’, Studia Math. 177 (2006), 81–96.CrossRefGoogle Scholar
[7]Ghahramani, F. and Loy, R. J., ‘Generalized notions of amenability’, J. Funct. Anal. 208(1) (2004), 229–260.CrossRefGoogle Scholar
[8]Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis, Vol. II (Springer, Berlin, 1970).Google Scholar
[9]Jewett, R. I., ‘Spaces with an abstract convolution of measures’, Adv. Math. 18 (1975), 1–110.CrossRefGoogle Scholar
[10]Johnson, B. E., ‘Cohomology in Banach algebras’, Mem. Amer. Math. Soc. 127 (1972).Google Scholar
[11]Murphy, G. J., C *-Algebras and Operator Theory (Academic Press, San Diego, CA, 1990).Google Scholar
[12]Runde, V., Lectures on Amenability, Lecture Notes in Mathematics, 1774 (Springer, Berlin, 2002).CrossRefGoogle Scholar
[13]Vrem, R. C., ‘Harmonic analysis on compact hypergroups’, Pacific J. Math. 85(1) (1979), 239–251.CrossRefGoogle Scholar