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arXiv · 0706.2664

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

Eva A. Gallardo-Gutiérrez·Maria J. González·Pekka Nieminen·Eero Saksman
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Abstract

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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Eva A. Gallardo-Gutiérrez, Maria J. González, Pekka Nieminen, Eero Saksman. 2007-06-18. On the connected component of compact composition operators on the Hardy space. https://arxiv.org/abs/0706.2664

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