MODULE APPROXIMATE AMENABILITY OF BANACH ALGEBRAS

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POURMAHMOOD AGHABABA HASAN; BODAGHI ABASALT

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Paper Information

Journal: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY Year:2013 | Volume:39 | Issue:6 Page(s): 1137-1158

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Title

MODULE APPROXIMATE AMENABILITY OF BANACH ALGEBRAS

Author(s)

POURMAHMOOD AGHABABA HASAN | BODAGHI ABASALT | Issue Writer Certificate

Keywords

APPROXIMATELY INNER

INVERSE SEMIGROUP

MODULE AMENABILITY

MODULE DERIVATION

Abstract

In the present paper, the concepts of module (uni- form) approximate amenability and contractibility of Banach al- gebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same properties. It is also shown that module uniform approximate (contractibility) amenability and module (contractibility, respectively) amenability for commutative Banach modules are equivalent. Applying these results to l1 (S) as an l1 (E) -module, for an INVERSE SEMIGROUP S with the set of idem- potents E, it is shown that l1 (S) is module approximately amenable (contractible) if and only if it is module uniformly approximately amenable if and only if S is amenable. Moreover, l1 (S)** is module (uniformly) approximately amenable if and only if a maximal group homomorphic image of S is finite.

Cites

GENERALIZED APPROXIMATE AMENABILITY OF DIRECT SUM OF BANACH ALGEBRAS

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APA: Copy

POURMAHMOOD AGHABABA, HASAN, & BODAGHI, ABASALT. (2013). MODULE APPROXIMATE AMENABILITY OF BANACH ALGEBRAS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 39(6), 1137-1158. SID. https://sid.ir/paper/613001/en

Vancouver: Copy

POURMAHMOOD AGHABABA HASAN, BODAGHI ABASALT. MODULE APPROXIMATE AMENABILITY OF BANACH ALGEBRAS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2013;39(6):1137-1158. Available from: https://sid.ir/paper/613001/en

IEEE: Copy

HASAN POURMAHMOOD AGHABABA, and ABASALT BODAGHI, “MODULE APPROXIMATE AMENABILITY OF BANACH ALGEBRAS,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 39, no. 6, pp. 1137–1158, 2013, [Online]. Available: https://sid.ir/paper/613001/en

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