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

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dc.creatorGallardo-Gutiérrez, Eva A.
dc.creatorGonzález, Maria J.
dc.creatorNieminen, Pekka
dc.creatorSaksman, Eero
dc.date2007-06-18
dc.date.accessioned2026-07-07T08:10:58Z
dc.date.available2026-07-07T08:10:58Z
dc.descriptionWe 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.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/0706.2664
dc.identifierhttp://arxiv.org/abs/0706.2664
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131980
dc.subjectFunctional Analysis
dc.subjectComplex Variables
dc.subject47B33 (Primary), 30D55, 47B38 (Secondary)
dc.titleOn the connected component of compact composition operators on the Hardy space
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