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

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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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Dates and versions

hal-01987504 , version 1 (21-01-2019)

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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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