Morita equivalence for Banach algebras

Abstract

We develop a theory for Morita equivalence of Banach algebras with bounded approximate identities and categories of essential modules, using functors compatible with the topology. Many aspects of discrete theory are carried over. Most importantly, the Eilenberg-Watts theorem holds, so that equivalence functors are representable as tensor functors. This enables us to determine how Banach algebras which are Morita equivalent to a given Banach algebra are constructed. It also leads to Morita invariance of bounded Hochschild homology, thus providing an efficient tool for computation of homology groups.