Geodesic
Description of the cohomology of Banach algebras and locally convex algebras in the language of $A_\infty$-structures
Izvestiya. Mathematics , Tome 62 (1998) no. 4, pp. 789-805.

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We consider the following problem: how can one apply the methods employed for describing the cohomology of algebras and based on the use of the $A_\infty$-structures of Stasheff to describe the cohomology of Banach algebras and locally convex algebras. 
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V. A. Smirnov; S. V. Kuznetsova; I. V. Mayorova. Description of the cohomology of Banach algebras and locally convex algebras in the language of $A_\infty$-structures. Izvestiya. Mathematics , Tome 62 (1998) no. 4, pp. 789-805. http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a5/

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