MORITA EQUIVALENCE FOR OPERATOR SYSTEMS

In ring theory, Morita equivalence preserves many properties of the objects, and generalizes the isomorphism equivalence between commutative rings. A strong Morita equivalence for selfadjoint operator algebras was introduced by Rieffel in the 60s, and works as a correspondence between their representations. In the past 30 years, a similar theory for non-selfadjoint operator algebras and operator spaces has been developed with much success, and we will review its main points in this talk. Then, taking motivation from the recent work of Connes and van Suijlekom, we will present Morita theory for operator systems. We will give equivalent characterizations of Morita equivalence via Morita contexts, bihomomoprhisms and stable isomorphisms, highlighting preserved properties. Time permitting, we will provide applications to rigid systems, function systems and non-commutative graphs. This is joint work with George Eleftherakis and Ivan Todorov.