Comparison of singular numbers of composition operators on different Hilbert spaces of analytic functions
We compare the rate of decay of singular numbers of a given composition operator acting on various Hilbert spaces of analytic functions on the unit disk D. We show that for the Hardy and Bergman spaces, our results are sharp. We also give lower and upper estimates of the singular numbers of the comp...
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| Published in | Journal of functional analysis Vol. 280; no. 3; p. 108834 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
01.02.2021
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| Online Access | Get full text |
| ISSN | 0022-1236 1096-0783 1096-0783 |
| DOI | 10.1016/j.jfa.2020.108834 |
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| Abstract | We compare the rate of decay of singular numbers of a given composition operator acting on various Hilbert spaces of analytic functions on the unit disk D. We show that for the Hardy and Bergman spaces, our results are sharp. We also give lower and upper estimates of the singular numbers of the composition operator with symbol the “cusp map” and the lens maps, acting on weighted Dirichlet spaces. |
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| AbstractList | We compare the rate of decay of singular numbers of a given composition operator acting on various Hilbert spaces of analytic functions on the unit disk D. We show that for the Hardy and Bergman spaces, our results are sharp. We also give lower and upper estimates of the singular numbers of the composition operator with symbol the “cusp map” and the lens maps, acting on weighted Dirichlet spaces. |
| ArticleNumber | 108834 |
| Author | Rodríguez-Piazza, Luis Lefèvre, Pascal Li, Daniel Queffélec, Hervé |
| Author_xml | – sequence: 1 givenname: Pascal orcidid: 0000-0001-9351-1798 surname: Lefèvre fullname: Lefèvre, Pascal email: pascal.lefevre@univ-artois.fr organization: Univ. Artois, Laboratoire de Mathématiques de Lens (LML) UR 2462, & Fédération Mathématique des Hauts-de-France FR 2037 CNRS, Faculté Jean Perrin, Rue Jean Souvraz, S.P. 18, F-62 300 Lens, France – sequence: 2 givenname: Daniel surname: Li fullname: Li, Daniel email: daniel.li@univ-artois.fr organization: Univ. Artois, Laboratoire de Mathématiques de Lens (LML) UR 2462, & Fédération Mathématique des Hauts-de-France FR 2037 CNRS, Faculté Jean Perrin, Rue Jean Souvraz, S.P. 18, F-62 300 Lens, France – sequence: 3 givenname: Hervé surname: Queffélec fullname: Queffélec, Hervé email: Herve.Queffelec@univ-lille.fr organization: Univ. Lille Nord de France, USTL, Laboratoire Paul Painlevé U.M.R. CNRS 8524 & Fédération Mathématique des Hauts-de-France FR 2037 CNRS, F-59 655 Villeneuve d'Ascq Cedex, France – sequence: 4 givenname: Luis surname: Rodríguez-Piazza fullname: Rodríguez-Piazza, Luis email: piazza@us.es organization: Universidad de Sevilla, Facultad de Matemáticas, Departamento de Análisis Matemático & IMUS, Calle Tarfia s/n, 41 012 Sevilla, Spain |
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| Keywords | secondary Approximation numbers Hilbert spaces of analytic functions Schatten classes Composition operator primary |
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| Title | Comparison of singular numbers of composition operators on different Hilbert spaces of analytic functions |
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