module-amenability on module extension banach algebras
Authors
abstract
let a be a banach algebra and e be a banach a-bimodule then s = a e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension banach algebra s = l1(es) l1(s) is △-amenable as a l1(es)-module if and only if l1(es) is amenable as banach algebra.
similar resources
Module-Amenability on Module Extension Banach Algebras
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 equipped with 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...
full textModule Amenability of module dual Banach algebras
In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe...
full textOn module extension Banach algebras
Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. Then ${mathcal{S}}=A oplus X$, the $l^1$-direct sum of $A$ and $X$ becomes a module extension Banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ In this paper, we investigate biflatness and biprojectivity for these Banach algebras. We also discuss on automatic continuity of derivations on ${mathcal{S...
full textApproximate $n-$ideal amenability of module extension Banach algebras
Let $mathcal{A}$ be a Banach algebra and $X$ be a Banach $mathcal{A}-$bimodule. We study the notion of approximate $n-$ideal amenability for module extension Banach algebras $mathcal{A}oplus X$. First, we describe the structure of ideals of this kind of algebras and we present the necessary and sufficient conditions for a module extension Banach algebra to be approximately n-ideally amenable.
full textCyclic amenability of Lau product and module extension Banach algebras
Recently, some results have been obtained on the (approximate) cyclic amenability of Lau product of two Banach algebras. In this paper, by characterizing of cyclic derivations on Lau product and module extension Banach algebras, we present general necessary and sufficient conditions for those to be (approximate) cyclic amenable. This not only provides new results on (approximate) cyclic amenabi...
full textOn (σ, τ)-module extension Banach algebras
Let A be a Banach algebra and X be a Banach A-bimodule. In this paper, we define a new product on $Aoplus X$ and generalize the module extension Banach algebras. We obtain characterizations of Arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new Banach algebra.
full textMy Resources
Save resource for easier access later
Journal title:
journal of linear and topological algebra (jlta)جلد ۱، شماره ۰۲، صفحات ۱۱۱-۱۱۴
Keywords
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023