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Weak$$^*$$-continuous derivations in dual Banach algebras. (English) Zbl 1274.46098
Let $$\mathcal {A}$$ be a dual Banach algebra and $$H^1_{w^{*}}(\mathcal {A},\mathcal {A})$$ be its first weak$$^{*}$$-continuous cohomology group with coefficients in $$\mathcal {A}$$. Several specific examples are indicated in which $$H^1_{w^{*}}(\mathcal {A},\mathcal {A})=\{0\}$$. A typical example is $$\mathcal {A}=M(G)$$, where $$M(G)$$ is the dual algebra of a locally compact topological group.

##### MSC:
 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
##### Keywords:
Arens product; 2-weakly amenable; derivation
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