# Two remarks on composition operators on the Dirichlet space

* Corresponding author
Abstract : We show that the decay of approximation numbers of compact composition operators on the Dirichlet space $\mathcal{D}$ can be as slow as we wish, which was left open in the cited work. We also prove the optimality of a result of O.~El-Fallah, K.~Kellay, M.~Shabankhah and A.~Youssfi on boundedness on $\mathcal{D}$ of self-maps of the disk all of whose powers are norm-bounded in $\mathcal{D}$.
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Cited literature [18 references]

https://hal-univ-artois.archives-ouvertes.fr/hal-00982257
Contributor : Daniel Li <>
Submitted on : Thursday, July 10, 2014 - 5:13:53 PM
Last modification on : Thursday, September 27, 2018 - 2:58:02 PM
Long-term archiving on : Friday, October 10, 2014 - 12:30:52 PM

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### Identifiers

• HAL Id : hal-00982257, version 2
• ARXIV : 1404.6035

### Citation

Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. Two remarks on composition operators on the Dirichlet space. 2014. ⟨hal-00982257v2⟩

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