| Abstrakt: |
In this paper, we introduce a new notion of module strong pseudo-amenability for Banach algebras. We study the relation between this new concept to other various notions at this issue, module pseudo-contractibility, module pseudo-amenability and module approximate amenability. For an inverse semigroup S with the set of all idempotents E , we show that ℓ 1 (S) is module strong pseudo-amenable as an ℓ 1 (E) -module if and only if S is amenable. For specific types of semigroups such as Brandt semigroups and bicyclic semigroups, we investigate the module strong pseudo-amenability of ℓ 1 (S). We show that for every non-empty set I , I (ℂ) under this new notion is forced to have a finite index as an -module, where = { [ a i , j ] ∈ Λ (ℂ) | ∀ i ≠ j , a i , j = 0 }. [ABSTRACT FROM AUTHOR] |
