Document Type : Research Paper

Authors

• Hamid Sadeghi
• Mahmmod Lashkarizadeh

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

Abstract

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

Keywords

• Banach algebra
• $varphi$-commutative
• $varphi$-derivation
• $varphi$-weakly amenability