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## On approximation numbers of composition operators

Daniel Li
Hervé Queffélec
• Function : Author
• PersonId : 859618
Luis Rodriguez-Piazza
• Function : Author
• PersonId : 859619

#### 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.

#### Domains

Mathematics [math] Functional Analysis [math.FA]

### Dates and versions

hal-00588256 , version 1 (22-04-2011)

### Identifiers

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

### Cite

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

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