$\Delta$-weak character amenability of certain Banach algebras

Abstract

In this paper we introduce the notion of $\Delta$-weak character amenable Banach algebras and investigate $\Delta$-weak character amenability of certain Banach algebras such as projective tensor product $A\hat{\otimes }B$, Lau product $A{\times }_{T}B$ for every Banach algebra $A$ and $B$, where $T$ be a homomorphism from $B$ into $A$, abstract Segal algebras and module extension Banach algebras.