The Structure of φ-Module Amenable Banach Algebras
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/176736 |
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| Summary: | 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 l1S is a commutative Banach l1E-module, then l1S** is φ**-module amenable if and only if S is finite, when φ∈Homl1El1S is an epimorphism. Indeed, we have generalized a well-known result due to Ghahramani et al. (1996). |
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| ISSN: | 1085-3375 1687-0409 |