Hochschild cohomology and perturbations of Banach algebras

Abstract

AbstractLet A and B be Banach algebras with identity and let π: A → B be a continuous homomorphism. We obtain conditions on the Hochschild cohomology of A under which perturbations of π are similar to π. We also show that if A is a Banach algebra such that H2(A, A) = H3(A, A) = 0, then perturbations of the multiplication of A give algebras isomorphic to A. We use our techniques to partially answer some problems of Kadison and Kastler on perturbations of operator algebras