Abstract
Let 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 H 2( A, A) = H 3( 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.
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