Derivations on generalized semidirect products of Banach algebras (Q307002)

Let \(A\) and \(B\) be two Banach algebras and \(I\) be a closed ideal of \(B\). Let further \(\theta:A\rightarrow B\) be a continuous Banach algebra homomorphism. The author considers a Banach algebra structure of an amalgamated algebra of \(A\) with \(B\) along \(I\) with respect to \(\theta\). He characterizes the derivations on this algebra and gives the first cohomology group of that under certain conditions.