Morita equivalence for self-induced Banach algebras

A Banach algebra A is self-induced, if [GRAPHICS] We extend our previous theory for Morita equivalence from the class of Banach algebras with bounded two-sided approximate identities to the class of self-induced Banach algebras. In the extended theory we still have the Eilenberg-Watts theorem and Morita invariance of bounded Hochschild homology. It provides a framework, where induced representations can be thoroughly discussed and where a Banach version of the Brauer group for a commutative Banach algebra can be defined.