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arXiv · 1706.03570

Some examples of composition operators and their approximation numbers on the Hardy space of the bi-disk

Daniel Li·Hervé Queffélec·Luis Rodríguez-Piazza
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Abstract

We give examples of composition operators $C\_\Phi$ on $H^2 (\D^2)$ showing that the condition $\|\Phi \|\_\infty = 1$ is not sufficient for their approximation numbers $a\_n (C\_\Phi)$ to satisfy $\lim\_{n \to \infty} [a\_n (C\_\Phi) ]^{1/\sqrt{n}} = 1$, contrary to the $1$-dimensional case. We also give a situation where this implication holds. We make a link with the Monge-Amp\`ere capacity of the image of $\Phi$.

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Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza. 2017-06-12. Some examples of composition operators and their approximation numbers on the Hardy space of the bi-disk. https://arxiv.org/abs/1706.03570

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