Weak amenability of semigroup algebras modulo an ideal

Abstract

The main purpose of this paper is to investigate weak amenability of semigroup algebras. We relate this to a new notion of weak amenability modulo an ideal of Banach algebras. As an important result, we show that $l^1(S)$ is weakly amenable modulo $I_{\sigma}$, where $I_{\sigma}$ is the corresponding ideal of the group congruence $\sigma$.