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 .
@article{arxiv.1711.05047,
title = {Closed Range Composition Operators on Hardy Spaces},
author = {Petros Galanopoulos and Kostas Panteris},
journal= {arXiv preprint arXiv:1711.05047},
year = {2020}
}