Weak$^*$-continuous derivations in dual Banach algebras
Weak$^*$-continuous derivations in dual Banach algebras
Let $\mathcal{A}$ be a dual Banach algebra. We investigate the first weak$^*$-continuous cohomology group of $\mathcal{A}$ with coefficients in $\mathcal{A}$. Hence, we obtain conditions on ${\mathcal{A}}$ for which \[ H^1_{w^*}(\mathcal{A}, \mathcal{A})=\lbrace 0\rbrace \,. \]