Title :

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

Author(s) :

Li, Daniel [Auteur]
Laboratoire de Mathématiques de Lens [LML]
Queffélec, Hervé [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rodríguez-Piazza, Luis [Auteur]

English keyword(s) :

Key-words: approximation numbers
Bergman space
bidisk
Composition operator
Green capacity
Hardy space
Monge-Ampère capacity
weighted composition operator
composition oper- ator
weighted compo- sition operator

HAL domain(s) :

Mathématiques [math]/Analyse fonctionnelle [math.FA]

English abstract : [en]

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 ...
Show more >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 $\Phi$.Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T17:34:29Z