Abstract and Applied Analysis

The Structure of φ -Module Amenable Banach Algebras

Mahmood Lashkarizadeh Bami, Mohammad Valaei, and Massoud Amini

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We study the concept of φ -module amenability of Banach algebras, which are Banach modules over another Banach algebra with compatible actions. Also, we compare the notions of φ -amenability and φ -module amenability of Banach algebras. As a consequence, we show that, if S is an inverse semigroup with finite set E of idempotents and l 1 S is a commutative Banach l 1 E -module, then l 1 S * * is φ * * -module amenable if and only if S is finite, when φ H o m l 1 E l 1 S is an epimorphism. Indeed, we have generalized a well-known result due to Ghahramani et al. (1996).

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Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 176736, 7 pages.

First available in Project Euclid: 27 February 2015

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Bami, Mahmood Lashkarizadeh; Valaei, Mohammad; Amini, Massoud. The Structure of $\phi $ -Module Amenable Banach Algebras. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 176736, 7 pages. doi:10.1155/2014/176736. https://projecteuclid.org/euclid.aaa/1425049574

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