Self-induced Banach algebras
Niels Grønbæk
Abstract
A Banach algebra A is self-induced if the multiplication is an isomorphism from the A-balanced projective tensor-square of A to A. The class of self-induced Banach algebras is a natural generalization of unital Banach algebras, providing a fertile framework for developing homological aspects of unital Banach algebras. Elementary results with applictions to computations of the bounded Hochschild cohomology groups H1(A,A*) with emphasis on A=A(X), the approximable operators on a Banach space X, are given.
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