Adjoints of rationally induced composition operators

TL;DR

This paper provides an elementary proof of a formula for the adjoint of rationally induced composition operators on Hardy space H^2, discusses variants, and explores conditions for compact perturbations.

Contribution

It offers a simplified proof of a recent formula and analyzes conditions under which the adjoint is a compact perturbation of a weighted composition operator.

Findings

Elementary proof of the adjoint formula

Variants and implications of the formula

Sufficient condition for compact perturbation

Abstract

We give an elementary proof of a formula recently obtained by Hammond, Moorhouse, and Robbins for the adjoint of a rationally induced composition operator on the Hardy space H^2. We discuss some variants and implications of this formula, and use it to provide a sufficient condition for a rationally induced composition operator adjoint to be a compact perturbation of a weighted composition operator.