Abstract
Abstract In this article, following Gorgi and Yazdanpanah, we define two new concepts of the ideal amenability for a Banach algebra A. We compare these notions with J-weak amenability and ideal amenability, where J is a closed two-sided ideal in A. We also study the hereditary properties of quotient ideal amenability for Banach algebras. Some examples show that the concepts of A/J-weak amenability and of J-weak amenability do not coincide for Banach algebras in general.
Highlights
The notion of amenability for Banach algebras was first introduced by B.E
We study the hereditary properties of quotient ideal amenability for
Since the notion of amenability was considered, several generalizations of this concept related to ideals such as weak amenability [2], ideal amenability [3], ideal Connes-amenability [4] etc. were introduced for Banach algebras
Summary
The notion of amenability for Banach algebras was first introduced by B.E. Johnson [1] in 1972. Banach algebra A is weakly amenable if every bounded derivation from A into A* is inner, or equivalently if H1(A, A*) = {0}. A Banach algebra A is I-weakly amenable if H1(A, I*) = {0} and is ideally amenable if it is We consider derivations into annihilators of the closed ideals of Banach algebras.
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