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

By Eva A. Gallardo-Guti'errez, María José González, Pekka J. Nieminen, Eero Saksman. 2007

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

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/f3b21ac9e9aaaa666c62ed0b12598d1369809c86