2026-06-29T08:02:35Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/505952024-07-12T14:37:29Zcom_20.500.14352_14col_20.500.14352_15
On the connected component of compact composition operators on the Hardy space
Gallardo Gutiérrez, Eva Antonia
González, María J.
Nieminen, Pekka J.
Saksman, Eero
517
Composition operators
Aleksandrov-Clark measures
Compact operator
Análisis matemático
1202 Análisis y Análisis Funcional
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.
Plan Nacional I+D
Gobierno de Aragon research group Analisis Matematico y Aplicaciones
Finnish Graduate School in Mathematical Analysis
Academy of Finland
Depto. de Análisis Matemático y Matemática Aplicada
Fac. de Ciencias Matemáticas
TRUE
pub
2023-06-20T10:34:24Z
2023-06-20T10:34:24Z
2008
journal article
https://hdl.handle.net/20.500.14352/50595
0001-8708
10.1016/j.aim.2008.06.005
eng
MTM2007-61446
MTM2005-00544
2005SGR00774
DGA E-64
118422
113826
118765
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.
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