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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, vol. 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), vol. 41, Dordrecht: Kluwer Academic Publishers Group, ISBN 978-0-7923-0217-9, MR 1093462
Khelemskii, A.Ya. (2001) [1994], "Cohomology of Banach algebras", Encyclopedia of Mathematics, EMS Press

Functional analysis (topics – glossary)

Spaces

Banach Besov Fréchet Hilbert Hölder Nuclear Orlicz Schwartz Sobolev Topological vector
Properties	Barrelled Complete Dual (Algebraic/Topological) Locally convex Reflexive Separable

Theorems

Operators

Algebras

Open problems

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