Weak amenability of Banach algebras with respect to characters

Abstract

For a Banach algebra ${\cal A}$, we introduce and investigate weak amenability of ${\cal A}$ with respect to a character. We give some necessary conditions for the weak amenability of $\cal A$ with respect to a character and describe a class of Banach algebras that are not weakly amenable with respect to characters. Finally, we give examples of Banach algebras which are weakly amenable with respect to characters but neither weakly amenable nor amenable with respect to characters.