Duality of $W^{\ast }$-correspondences and applications

Abstract

This is an exposition of our work on the canonical models of representations of Hardy algebras associated with $W^{\ast }$-correspondences. It generalizes the model theory of Sz.-Nagy and Foias and the work of Popescu on models of row contractions. We also emphasize the concept of duality for $W^{\ast }$-correspondences and its relation to Morita equivalence of correspondenses.

Expository, 18 pages