On the connected component of compact composition operators on the Hardy space
Functional Analysis
2007-06-20 v1 Complex Variables
Abstract
We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space on the unit disc. This answers a question posed by Shapiro and Sundberg in 1990. We also establish an improved version of a theorem of MacCluer, giving a lower bound for the essential norm of a difference of composition operators in terms of the angular derivatives of their symbols. As a main tool we use Aleksandrov-Clark measures.
Cite
@article{arxiv.0706.2664,
title = {On the connected component of compact composition operators on the Hardy space},
author = {Eva A. Gallardo-Gutiérrez and Maria J. González and Pekka Nieminen and Eero Saksman},
journal= {arXiv preprint arXiv:0706.2664},
year = {2007}
}