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Keywords:
Arens product; 2-weakly amenable; derivation
Arens product; 2-weakly amenable; derivation
Summary:
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
\[ H^1_{w^*}(\mathcal{A}, \mathcal{A})=\lbrace 0\rbrace \,. \]
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