Nevanlinna–Pick Type Interpolation in a Dual Algebra

The duality approach of Sarason, Abrahamse, Ball, and others is extended to obtain a verion of Nevanlinna–Pick interpolation for a weak star closed algebra of operators on Hilbert space. In this context factorization is the polar decomposition of a positive trace class operator. Several concrete Nevanlinna–Pick type theorems are seen to follow from the main result and various versions of the Wold decomposition.