2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70886This is an exposition of our work on the canonical models of representations of Hardy algebras associated with $W^*$-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 $W^*$-correspondences and its relation to Morita equivalence of correspondenses.Expository, 18 pagesOperator Algebras46L08, 46L53, 47A45, 47L55, 47L65, 47L75text