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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| Format: | Article |
| Language: | English |
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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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| author | Mahmood Lashkarizadeh Bami Mohammad Valaei Massoud Amini |
| author_facet | Mahmood Lashkarizadeh Bami Mohammad Valaei Massoud Amini |
| author_sort | Mahmood Lashkarizadeh Bami |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-f3942f529a2d4da9b1b369b85c106656 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f3942f529a2d4da9b1b369b85c1066562025-02-03T01:31:11ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/176736176736The Structure of φ-Module Amenable Banach AlgebrasMahmood Lashkarizadeh Bami0Mohammad Valaei1Massoud Amini2Department of Mathematics, University of Isfahan, Isfahan, IranDepartment of Mathematics, University of Isfahan, Isfahan, IranDepartment of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, IranWe 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).http://dx.doi.org/10.1155/2014/176736 |
| spellingShingle | Mahmood Lashkarizadeh Bami Mohammad Valaei Massoud Amini The Structure of φ-Module Amenable Banach Algebras Abstract and Applied Analysis |
| title | The Structure of φ-Module Amenable Banach Algebras |
| title_full | The Structure of φ-Module Amenable Banach Algebras |
| title_fullStr | The Structure of φ-Module Amenable Banach Algebras |
| title_full_unstemmed | The Structure of φ-Module Amenable Banach Algebras |
| title_short | The Structure of φ-Module Amenable Banach Algebras |
| title_sort | structure of φ module amenable banach algebras |
| url | http://dx.doi.org/10.1155/2014/176736 |
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