Resumen de Semigroups of compressed Teoplitz operators and Nevalinna - Pick interpolation

Steven M. Seubert

• The purpose of this paper is to determine conditions for an operator commuting with the compression S of the standard unilateral shift on the Hardy space to a shift coinvariant subspace H(B) to embed in a semigroup of operators commuting with S. For B an interpolating Blaschke product, a necessary and sufficient condition is that a symbol of the operator and B have no common zeroes. The condition is shown to be necessary for an arbitrary inner function, but not sufficient for any interpolating Blaschke product. For B an interpolating Blaschke product, necessary and sufficient conditions are given for an operator commuting with S to embed in a semigroup of operators commuting with S consisting entirely of contraction operators using the Nevanlinna-Pick Interpolation Theorem.