Abstract
Let and be Banach algebras, let be a continuous Banach algebra homomorphism, and let be a closed ideal in . Then the -direct sum of and with a special product becomes a Banach algebra, denoted by , which we call the generalized semidirect product of and . In this article, among other things, we first characterize derivations on and then we compute the first cohomology group of when the first cohomology groups of with coefficients in and are trivial. As an application we characterize the first cohomology group of second duals of dual Banach algebras. Then we provide a nice characterization of the first cohomology group of . Furthermore, we calculate the first cohomology group of some concrete Banach algebras related to locally compact groups.
Citation
Hasan Pourmahmood Aghababa. "Derivations on generalized semidirect products of Banach algebras." Banach J. Math. Anal. 10 (3) 509 - 522, July 2016. https://doi.org/10.1215/17358787-3607156
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