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## Two remarks on composition operators on the Dirichlet space

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Daniel Li

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Hervé Queffélec
• Function : Author
• PersonId : 916881
Luis Rodriguez-Piazza
• Function : Author
• PersonId : 859619

#### 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 $\mathcal{D}$.

#### Domains

Mathematics [math] Functional Analysis [math.FA]

### Dates and versions

hal-00982257 , version 1 (23-04-2014)
hal-00982257 , version 2 (10-07-2014)

### Identifiers

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

### Cite

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

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