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).
Mahmood Lashkarizadeh Bami. Mohammad Valaei. Massoud Amini. "The Structure of -Module Amenable Banach Algebras." Abstr. Appl. Anal. 2014 (SI49) 1 - 7, 2014. https://doi.org/10.1155/2014/176736