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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 176736, 7 pages
http://dx.doi.org/10.1155/2014/176736
Research Article

The Structure of -Module Amenable Banach Algebras

1Department of Mathematics, University of Isfahan, Isfahan, Iran
2Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Iran
3School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5746, Iran

Received 14 November 2013; Accepted 4 February 2014; Published 2 April 2014

Academic Editor: Erdal Karapınar

Copyright © 2014 Mahmood Lashkarizadeh Bami et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the concept of -module amenability of Banach algebras, which are Banach modules over another Banach algebra with compatible actions. Also, we compare the notions of -amenability and -module amenability of Banach algebras. As a consequence, we show that, if is an inverse semigroup with finite set of idempotents and is a commutative Banach -module, then is -module amenable if and only if is finite, when is an epimorphism. Indeed, we have generalized a well-known result due to Ghahramani et al. (1996).