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ULTRAPOWERS OF ℓ1-MUNN ALGEBRAS AND THEIR APPLICATION TO SEMIGROUP ALGEBRAS

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  25 January 2012

MAEDEH SOROUSHMEHR
MAEDEH SOROUSHMEHR*
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan 81746-73441, Iran (email: [email protected])
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Abstract

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In this work, we study and investigate the ultrapowers of ℓ1-Munn algebras. Then we show that the class of ℓ1-Munn algebras is stable under ultrapowers. Finally, applying this result to semigroup algebras, we show that for a semigroup S, ultra-amenability of ℓ1(S) and amenability of the second dual ℓ1(S)′′ are equivalent.

Keywords

Banach algebraultrapoweramenabilityℓ1-Munn algebra

MSC classification

Secondary: 46B08: Ultraproduct techniques in Banach space theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 3 , December 2012 , pp. 424 - 429
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

[1]Dales, H. G., Lau, A. T.-M. and Strauss, D., ‘Banach algebras on semigroups and their compactifications’, Mem. Amer. Math. Soc. 205 (2010), 1–165.Google Scholar
[2]Daws, M., ‘Ultrapowers of Banach algebras and modules’, J. Glasg. Math. 50 (2008), 539–555.CrossRefGoogle Scholar
[3]Daws, M., ‘Amenability of ultrapowers of Banach algebras’, Proc. Edinb. Math. Soc. 52 (2009), 307–338.CrossRefGoogle Scholar
[4]Daws, M., ‘Corrigendum: Amenability of ultrapowers of Banach algebras’, Proc. Edinb. Math. Soc. 53 (2010), 633–637.CrossRefGoogle Scholar
[5]Esslamzadeh, G. H., ‘Banach algebra structure and amenability of a class of matrix algebras with applications’, J. Funct. Anal. 161(2) (1999), 364–383.CrossRefGoogle Scholar
[6]Esslamzadeh, G. H. and Esslamzadeh, T., ‘Contractibility of ℓ 1-Munn algebras with applications’, Semigroup Forum 63(1) (2001), 1–10.CrossRefGoogle Scholar
[7]Heinrich, S., ‘Ultraproducts in Banach space theory’, J. reine angew. Math. 313 (1980), 72–104.Google Scholar
[8]Lau, A. T.-M., Loy, R. J. and Willis, G. A., ‘Amenability of Banach and C *-algebras on locally compact groups’, Studia Math. 119 (1996), 161–178.Google Scholar
[9]Munn, W. D., ‘On semigroup algebras’, Math. Proc. Cambridge Philos. Soc. 51 (1955), 1–15.CrossRefGoogle Scholar
[10]Shojaee, B., Esslamzadeh, G. H. and Pourabbas, A., ‘First order cohomology of ℓ 1-Munn algebras and certain semigroup algebras’, Bull. Iranian Math. Soc. 35(1) (2009), 211–219.Google Scholar