Composition operators on de Branges–Rovnyak spaces associated to a rational (not inner) function

Abstract

In this paper, we characterize the boundedness, the compactness and the Hilbert–Schmidt property for composition operators acting from a de Branges–Rovnyak space H(b) into itself, when b is a rational function in the closed unit ball of H∞ (but not a finite Blaschke product). In particular, we extend some of the results obtained by D. Sarason and J.N. Silva in the context of local Dirichlet spaces.