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arXiv · 1404.6035

Two remarks on composition operators on the Dirichlet space

Daniel Li·Hervé Queffélec·Luis Rodriguez-Piazza
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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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Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. 2014-07-10. Two remarks on composition operators on the Dirichlet space. https://arxiv.org/abs/1404.6035

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