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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Bibliographic Details
Published inJournal of functional analysis Vol. 280; no. 3; p. 108834
Main Authors Lefèvre, Pascal, Li, Daniel, Queffélec, Hervé, Rodríguez-Piazza, Luis
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.02.2021
Subjects
Approximation numbers
Composition operator
Hilbert spaces of analytic functions
Schatten classes
secondary
Approximation numbers
Hilbert spaces of analytic functions
Schatten classes
Composition operator
primary
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ISSN0022-1236
1096-0783
DOI10.1016/j.jfa.2020.108834

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Summary: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.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2020.108834