Weighted composition operators on de Branges-Rovnyak spaces

2025/12/17 by Emmanuel Fricain, Muath Karaki, Fricain, Emmanuel +5
Mathematics · #Holomorphic and Operator Theory #Advanced Banach Space Theory #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.2512.15287

Abstract

In this paper, we characterize the boundedness and the compactness of weighted composition operators acting on a de Branges-Rovnyak space \mathcal H(b), where the symbol b is a rational function in the unit ball of H^∞ that is not a finite Blaschke product. Our results extend those of [2] by exploiting a close relationship between weighted composition operators on \mathcal H(b) and their counterparts on the Hardy space H².

Citations

• Interpolation and random interpolation in de Branges-Rovnyak spaces
• Composition Operators On De Branges-rovnyak Spaces Associated To A Rational (Not Inner) Function
• Multipliers between range spaces of co-analytic Toeplitz operators
• Which de Branges–Rovnyak spaces are Dirichlet spaces (and vice versa)?
• Boundedness, compactness and Schatten-class membership of weighted composition operators

Related

• Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators
• Composition Operators On De Branges-rovnyak Spaces Associated To A Rational (Not Inner) Function
• Weighted Composition Operators from H^∞ to the Bloch Space in the Unit Ball of Cn
• Weighted composition operators on Hilbert function spaces on the ball
• Composition operators on Bergman-Orlicz spaces on the ball