2013/01/15 by Hasan Pourmahmood-Aghababa, Pourmahmood-Aghababa, Hasan, Abasalt Bodaghi +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1301.3241
arxiv created 2013/01/15 · openalex publication_date 2013/01/15 · arxiv updated 2013/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras 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 idempotents 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.