Title :

A spectral radius type formula for approximation numbers of composition operators

Author(s) :

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

English keyword(s) :

approximation numbers
Bergman space
composition operator
Dirichlet space
Green capacity
Hardy space
weighted analytic Hilbert space

HAL domain(s) :

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

English abstract : [en]

For approximation numbers $a_n (C_\phi)$ of composition operators $C_\phi$ on weighted analytic Hilbert spaces, including the Hardy, Bergman and Dirichlet cases, with symbol $\phi$ of uniform norm $< 1$, we prove that ...
Show more >For approximation numbers $a_n (C_\phi)$ of composition operators $C_\phi$ on weighted analytic Hilbert spaces, including the Hardy, Bergman and Dirichlet cases, with symbol $\phi$ of uniform norm $< 1$, we prove that $\lim_{n \to \infty} [a_n (C_\phi)]^{1/n} = \e^{- 1/ \capa [\phi (\D)]}$, where $\capa [\phi (\D)]$ is the Green capacity of $\phi (\D)$ in $\D$. This formula holds also for $H^p$ with $1 \leq p < \infty$.Show less >

Language :

Anglais

Comment :

25 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL