A spectral radius type formula for approximation numbers of composition operators
arXiv:1407.2171
Abstract
For approximation numbers $a_n (C_Ï)$ of composition operators $C_Ï$ on weighted analytic Hilbert spaces, including the Hardy, Bergman and Dirichlet cases, with symbol $Ï$ of uniform norm $< 1$, we prove that $\lim_{n \to \infty} [a_n (C_Ï)]^{1/n} = \e^{- 1/ \capa [Ï(\D)]}$, where $\capa [Ï(\D)]$ is the Green capacity of $Ï(\D)$ in $\D$. This formula holds also for $H^p$ with $1 \leq p < \infty$.
25 pages