Composition operators on Hardy spaces of a half plane

Abstract

We prove that a composition operator is bounded on the Hardy space $H^2$ of the right half-plane if and only if the inducing map fixes the point at infinity non-tangentially, and has a finite angular derivative $\lambda$ there. In this case the norm, essential norm, and spectral radius of the operator are all equal to $\sqrt{\lambda }$.

Cited by in corpus (6)

• Spectra of linear fractional composition operators on the Hardy and weighted Bergman spaces of the half-plane
• Dynamical properties for composition operators on $H^2({\mathbb{C}}_{+})$
• Complex symmetry of linear fractional composition operators on a half-plane
• Composition operators on Hardy-Smirnov spaces
• Composition operators on de Branges spaces of entire functions
• Dynamics for affine composition operators on weighted Bergman space of a half plane