Banach algebra cohomology

In mathematics, Banach algebra cohomology of a Banach algebra with coefficients in a bimodule is a cohomology theory defined in a similar way to Hochschild cohomology of an abstract algebra, except that one takes the topology into account so that all cochains and so on are continuous.

References

• Johnson, Barry Edward (1972), Cohomology in Banach algebras, Memoirs of the American Mathematical Society, 127, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1827-5, https://books.google.com/books?id=WgYuKl1Y340C 
• Helemskii, Alexander Ya. (1989), The homology of Banach and topological algebras, Mathematics and its Applications (Soviet Series), 41, Dordrecht: Kluwer Academic Publishers Group, ISBN 978-0-7923-0217-9, https://books.google.com/books?id=0897Z7xv_ksC 
• Hazewinkel, Michiel, ed. (2001), "Cohomology of Banach algebras", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=c/c023120