On the connected component of compact composition operators on the Hardy space
Abstract
We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space H2 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.
0