Closed Range Composition Operators on Hardy Spaces

TL;DR

This paper extends known results about when composition operators have closed range from the Hardy space H2 to the more general Hp spaces for p>0, broadening the understanding of their behavior.

Contribution

The paper generalizes existing criteria for closed range composition operators from H2 to all Hp spaces with p>0, providing a wider applicability of the theory.

Findings

Closed range criteria are extended to Hp spaces for p>0.

Results unify the understanding of composition operators across different Hardy spaces.

The extension confirms the robustness of known conditions beyond H2.

Abstract

We show that the already known results for a composition operator to have closed range on H2 (Cima, Thomson, and Wogen (1974), Zorboska (1994)) can be extended to Hp for p>0 .