# On approximation numbers of composition operators

Abstract : We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces $\mathfrak{B}_\alpha$ 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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Preprints, Working Papers, ...

https://hal-univ-artois.archives-ouvertes.fr/hal-00588256
Contributor : Daniel Li Connect in order to contact the contributor
Submitted on : Friday, April 22, 2011 - 3:29:55 PM
Last modification on : Thursday, September 16, 2021 - 10:25:57 AM
Long-term archiving on: : Saturday, July 23, 2011 - 2:42:36 AM

### Files

approximation_preprint.pdf
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### Identifiers

• HAL Id : hal-00588256, version 1
• ARXIV : 1104.4451

### Citation

Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. On approximation numbers of composition operators. 2011. ⟨hal-00588256⟩

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