Muhly and Solel developed a notion of Morita equivalence for C *correspondences, which they used to show that if two C * -correspondences E and F are Morita equivalent then their tensor algebras T + (E) and T + (F ) are (strongly) Morita equivalent operator algebras. We give the weak * version of this result by considering (weak) Morita equivalence of W * -correspondences and employing Blecher and Kashyap's notion of Morita equivalence for dual operator algebras. More precisely, we show that weak Morita equivalence of W * -correspondences E and F implies weak Morita equivalence of their Hardy algebras H ∞ (E) and H ∞ (F ). We give special attention to W * -graph correspondences and show a number of results related to their Morita equivalence.
Let E be a W * -correspondence and let H ∞ (E) be the associated Hardy algebra. The unit disc of intertwiners ((E ) * ) plays a central role in the study of H ∞ (E) . We show a number of results related to groups of automorphisms of both H ∞ (E) and ((E ) * ) . We find a matrix representation for these groups and describe several features of their algebraic structure. Furthermore, we show an application of Aut( ((E ) * )) to the study of Morita equivalence of W * -correspondences.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.