In this paper we define the module extension dual Banach algebras and we use this Banach algebras to finding the relationship between weak−continuous homomorphisms of dual Banach algebras and Connes-amenability. So we study the weak∗−continuous derivations on module extension dual Banach algebras.

Let G be a locally compact group, and let 1 < p < ∞. In this paper we investigate the injectivity of the left L1(G)-module Lp(G). We define a family of amenability type conditions called (p, q)-amenability, for any 1 ≤ p ≤ q. For a general locally compact group G we show if Lp(G) is injective, then G must be (p, p)-amenable. For a discrete group G we prove that l p(G) is injective if and only i...

We study amenability of algebras and modules (based on the notion of almost-invariant finite-dimensional subspace), and apply it to algebras associated with finitely generated groups. We show that a group G is amenable if and only if its group ring KG is amenable for some (and therefore for any) field K. Similarly, a G-set X is amenable if and only if its span KX is amenable as a KG-module for ...

It is now widely accepted that separating programs into modules is useful in program development and maintenance. While many Prolog implementations include useful module systems, we argüe that these systems can be improved in a number of ways, such as, for example, being more amenable to effective global analysis and transformation and allowing sepárate compilation or sensible creation of stand...

The concept of amenability for Banach algebras was introduced by Johnson in 1972 [6]. Several modifications of this notion, such as approximate amenability and pseudo-amenability, were introduced in [2] and [4]. In the current paper we investigate the pseudo-amenability of Brandt semigroup algebras. It was shown in [2] and [4] that for the group algebra L(G), amenability, approximate amenabilit...