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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: soroushmehr@math.ui.ac.ir)
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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

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