Module-Amenability on Module Extension Banach Algebras

Subject Areas : History and biography

D. Ebrahimi bagha ¹

1 - Department of Mathematics, Faculty of Science, Islamic Azad University, Centeral Tehran Branch, P. O. Box 13185/768, Tehran, Iran

Received: 2012-01-01 Accepted : 2012-01-01 Published : 2012-06-01

Keywords: module extension, Module-amenability, Banach algebras,

Abstract :

Let $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A \oplus E$,the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equippedwith the algebras product $(a,x).(a^\prime,x^\prime)= (aa^\prime, a.x^\prime+ x.a^\prime)$. In this paper, we investigate $\triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$with the set of idempotents $E_S$, the module extension Banach algebra $S=l^1(E_S)\oplus l^1(S)$ is $\triangle$-amenable as a $l^1(E_S)$-module if and only if $l^1(E_S)$ is amenable as Banach algebra.

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