Interpolation and Commutant Lifting with Weights

Our two principle goals are generalizations of the commutant lifting theorem and the Nevanlinna-Pick interpolation theorem to the context of Hardy algebras built from $W^*$-correspondences endowed with a sequence of weights. These theorems generalize theorems of Muhly and Solel from 1998 and 2004, respectively, which were proved in settings without weights. Of special interest is the fact that commutant lifting in our setting is a consequence of Parrott's Lemma; it is inspired by work of Arias.