A spectral radius type formula for approximation numbers of composition operators
For approximation numbers an(Cφ) of composition operators Cφ on weighted analytic Hilbert spaces, including the Hardy, Bergman and Dirichlet cases, with symbol φ of uniform norm <1, we prove that limn→∞[an(Cφ)]1/n=e−1/Cap[φ(D)], where Cap[φ(D)] is the Green capacity of φ(D) in D. This formula ho...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/46342 |
| Acceso en línea: | http://hdl.handle.net/11441/46342 https://doi.org/10.1016/j.jfa.2014.09.008 |
| Access Level: | acceso abierto |
| Palabra clave: | Approximation numbers Bergman space Composition operator Dirichlet space Green capacity Hardy space Weighted analytic Hilbert space |
| Sumario: | For approximation numbers an(Cφ) of composition operators Cφ on weighted analytic Hilbert spaces, including the Hardy, Bergman and Dirichlet cases, with symbol φ of uniform norm <1, we prove that limn→∞[an(Cφ)]1/n=e−1/Cap[φ(D)], where Cap[φ(D)] is the Green capacity of φ(D) in D. This formula holds also for Hp with 1≤p<∞. |
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