Approximate $n-$ideal amenability of module extension Banach algebras

Subject Areas : Functional analysis

M. Ettefagh ¹ , S. Etemad ²

1 - Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
2 - Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

Received: 2020-08-16 Accepted : 2020-09-24 Published : 2020-09-01

Keywords: amenability, ideal amenability, module extension Banach algebras,

Abstract :

Let $\mathcal{A}$ be a Banach algebra and $X$ be a Banach$\mathcal{A}-$bimodule. We study the notion of approximate $n-$idealamenability for module extension Banach algebras $\mathcal{A}\oplusX$. First, we describe the structure of ideals of this kind ofalgebras and we present the necessary and sufficient conditions fora module extension Banach algebra to be approximately n-ideallyamenable.

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