On approximation numbers of composition operators
We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces Bα of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they grow at least exponentially, and this speed of convergence is only obtained for symbols which do n...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/46366 |
| Acceso en línea: | http://hdl.handle.net/11441/46366 https://doi.org/10.1016/j.jat.2011.12.003 |
| Access Level: | acceso abierto |
| Palabra clave: | Approximation number Bergman space Carleson measure Composition operator Hardy space Interpolation sequence Reproducing kernel Weighted Bergman space Weighted shift |
| Sumario: | We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces Bα of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they grow at least exponentially, and this speed of convergence is only obtained for symbols which do not approach the unit circle. We also give an upper bounds and explicit an example. |
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