MORITA EQUIVALENCE FOR BANACH-ALGEBRAS

We develop a theory for Morita equivalence of Banach algebras with bou nded approximate identities and categories of essential modules, using functors compatible with the topology. Many aspects of discrete theor y are carried over. Most importantly, the Eilenberg-Watts theorem hold s, so that equivalence functors are representable as tenser functors. This enables us to determine how Banach algebras which are Morita equi valent to a given Banach algebra are constructed. It also leads to Mor ita invariance of bounded Hochschild homology, thus providing an effic ient tool for computation of homology groups.