%0 Journal Article
%T Homomorphism Weak amenability of certain Banach algebras
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Sadeghi, Hamid
%A Lashkarizadeh, Mahmmod
%D 2018
%\ 08/01/2018
%V 9
%N 1
%P 235-245
%! Homomorphism Weak amenability of certain Banach algebras
%K Banach algebra
%K $varphi$-commutative
%K $varphi$-derivation
%K $varphi$-weakly amenability
%R 10.22075/ijnaa.2018.1201.1276
%X 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.
%U https://ijnaa.semnan.ac.ir/article_3099_3c9686cd0612388fda1d7fbfe656ad40.pdf