Derivations into duals of closed ideals of Banach algebras

Abstract

Let $\mathcal{A}$ be a Banach algebra. We study those closed ideals $I$ of $\mathcal{A}$ for which the first cohomology group of $\mathcal{A}$ with coefficients in $I^{\ast }$ is trivial; i.e. $H^1(\mathcal{A},{\mathcal{I}}^{\ast })=\{0\}$. We investigate such closed ideals when $\mathcal{A}$ is weakly amenable or biflat. Also we give some hereditary properties of ideal amenability.