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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)
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