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

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https//doi.org/10.1016/j.aim.2008.06.005

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2008

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https://hdl.handle.net/20.500.14352/50595

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Gallardo Gutiérrez, E. A., et al. «On the Connected Component of Compact Composition Operators on the Hardy Space». Advances in Mathematics, vol. 219, n.o 3, octubre de 2008, pp. 986-1001. DOI.org (Crossref), https://doi.org/10.1016/j.aim.2008.06.005.

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. 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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Análisis matemático

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1202 Análisis y Análisis Funcional

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