Morita equivalence of w*-rigged modules

Abstract

The w*-rigged modules over dual operator algebras were introduced by Blecher and Kashyap as a generalization of W*-modules. In this paper, we introduce two new types of Morita equivalence between right w*-rigged modules over unital dual operator algebras and we examine whether these notions imply stable isomorphism between the corresponding modules. Furthermore, we investigate them in detail for the class of right w*-rigged modules over nest algebras, a class which was characterized by G.K. Eleftherakis.