Derivations on certain matrix algebras with applications to compact groups

Abstract

In this paper we characterize the derivations from $\frak E_p(\widehat{G})$ into $\frak E_q(\widehat{G})$, $1\leq p,q\leq\infty$. We find necessary and sufficient conditions for weak amenability of Banach algebras $\frak E_p(\widehat{G})$, $1\leq p\leq\infty$. Moreover we find a necessary condition for the weak amenability of the convolution Banach algebra $A(G)$ on a compact group $G$, where its sufficiency was proved earlier by Ghahramani and Lau.