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 cohains 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, MR 0374934 
• Helemskii, Alexander Ya. (1989) [1986], 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, MR 1093462 
• Khelemskii, A.Ya. (2001), "Cohomology of Banach algebras", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4