A spectral radius type formula for approximation numbers of composition operators

Abstract : 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 $1 \leq p < \infty$.
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Submitted on : Tuesday, July 8, 2014 - 3:15:59 PM
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  • HAL Id : hal-01020782, version 1
  • ARXIV : 1407.2171

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Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. A spectral radius type formula for approximation numbers of composition operators. 2014. ⟨hal-01020782⟩

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