# An extremal composition operator on the Hardy space of the bidisk with small approximation numbers

Abstract : We construct an analytic self-map $\Phi$ of the bidisk ${\mathbb D}^2$ whose image touches the distinguished boundary, but whose approximation numbers of the associated composition operator on $H^2 ({\mathbb D}^2)$ are small in the sense that $\limsup_{n \to \infty} [a_{n^2} (C_\Phi)]^{1 / n} < 1$.
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Cited literature [21 references]

https://hal-univ-artois.archives-ouvertes.fr/hal-01987504
Contributor : Daniel Li <>
Submitted on : Monday, January 21, 2019 - 11:02:12 AM
Last modification on : Thursday, October 1, 2020 - 12:48:08 PM

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Distinguished boundary.pdf
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### Identifiers

• HAL Id : hal-01987504, version 1
• ARXIV : 1901.07245

### Citation

Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza. An extremal composition operator on the Hardy space of the bidisk with small approximation numbers. 2019. ⟨hal-01987504⟩

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