Interpolation for upper triangular operators

In this paper the classical interpolation problems of Nevanlinna-Pick and Caratheodory-Fejer, as well as mixtures of the two, are solved in the general setting of upper triangular operators. Herein, the “points” at which the interpolation is carried out are themselves (diagonal) operators, and the components of all the intervening operators in their natural matrix representation may be finite or infinite dimensional. Moreover, we consider both contractive and strictly contractive solutions. A number of classical and new interpolation problems emerge as special cases.