Derivations into duals of closed ideals of Banach algebras

M. Eshaghi Gordji, B. Hayati, S. A. R. Hosseiniun

Published 2006-10-04, updated 2006-10-05Version 2

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