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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https://hal-univ-artois.archives-ouvertes.fr/hal-00588256
Contributor : Daniel Li <>
Submitted on : Friday, April 22, 2011 - 3:29:55 PM
Last modification on : Tuesday, July 3, 2018 - 11:27:57 AM
Long-term archiving on : Saturday, July 23, 2011 - 2:42:36 AM

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

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

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