Homomorphism Weak amenability of certain Banach algebras

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Science, University of Isfahan, Isfahan, Iran

Abstract

In this paper we introduce the notion of $\varphi$-commutativity for a Banach algebra $A$, where $\varphi$ is a continuous homomorphism on $A$ and study the concept of $\varphi$-weak amenability for $\varphi$-commutative Banach algebras. We give an example to show that the class of $\varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We characterize $\varphi$-weak amenability of $\varphi$-commutative Banach algebras and prove some hereditary properties. Moreover we verify some of the previous available results about commutative weakly amenable Banach algebras, for $\varphi$-commutative $\varphi$-weakly amenable Banach algebras.

Keywords

International Journal of Nonlinear Analysis and Applications
Volume 9, Issue 1
Summer and Autumn 2018
Pages 235-245

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