On the Connected Component of Compact Composition Operators on the Hardy Space
نویسندگان
چکیده
We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space H. 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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