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Composition Operators On De Branges-rovnyak Spaces Associated To A Rational (Not Inner) Function (2211.04864v1)
Published 9 Nov 2022 in math.FA
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 $\mathcal H(b)$ into itself, when $b$ is a rational function in the closed unit ball of $H\infty$ (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.