Derivations on the tensor product of Banach algebras

Abstract

In this paper, we study the ideal amenability of tensor product of Banach algebras. Among other things, we show that the ideal amenability $\mathcal A\widehat{\otimes}\mathcal B$ implies the ideal amenability of Banach algebras $\mathcal A$ and $\mathcal B$ for which character spaces of $\mathcal A$ and $\mathcal B$ are non-empty. Finally, we provide some examples in which $\mathcal A\widehat{\otimes}\mathcal B$ is ideally amenable.