On the connected component of compact composition operators on the Hardy space

Details On the connected component of compact composition operators on the Hardy space On the connected component of compact composition operators on the Hardy space

2007-06-18

arxiv.org/abs/0706.2664v1

Mathematics

Functional Analysis

16 pages

Scientific paper

We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space $H^2$ 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.

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