M.h. Sattari

Azarbaijan Shahid Madani University · Department of Mathematics

In this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric Connes amenability. We determine symmetric module amenability and symmetric Connes amenability of some concrete Banach algebras. Indeed, it is shown that ℓ1(S) is a symmetric ℓ1(E)-module amenable if and only if S is amenable, where S is an...

In this article, notion of n-derivations is introduced for all integer n > 2. Although all derivations are n-derivation, in general these are not equivalent. Some properties that are valued for ordinary derivations, are investigated for n-derivations such as Leibnitz rule and Singer-Wermer theorem. Also, we show that under certain condition n-deriv...

Let A and B be Banach algebras and M be a Banach ( A, B)-module. Then, T = [GRAPHICS] equipped with the usual 2 x 2 matrix operations, obvious internal module actions and the Banach space norm [GRAPHICS] = parallel to a parallel to(A) + parallel to m parallel to(M) + parallel to b parallel to(B) is a triangular Banach algebra. We show that T is bif...

We extend the concept of Arens regularity of a Banach algebra to the case that there is an -module structure on , and show that when S is an inverse semigroup with totally ordered subsemigroup E of idempotents, then A=ℓ 1(S) is module Arens regular if and only if an appropriate group homomorphic image of S is finite. When S is a discrete grou...

Let A be a C ∗-algebra and I be a closed ideal of A. we show that A is n-I-weakly amenable for each n ∈ N i.e. H1(A,I(n)) = 0. This result generalize the fact that asserts all C ∗-algebras are ideally amenable.