Comparison of singular numbers of composition operators on different Hilbert spaces of analytic functions

Hervé Queffélec (1) , Pascal Lefèvre (2) , Daniel Li (2) , Luis Rodriguez-Piazza (3)

1 LPP - Laboratoire Paul Painlevé
2 LML - Laboratoire de Mathématiques de Lens
3 Departamento de Analisis Matematico

We compare the rate of decay of singular numbers of a given composition operator acting on various Hilbert spaces of analytic functions on the unit disk $\D$. We show that for the Hardy and Bergman spaces, our results are sharp. We also give lower and upper estimates of the singular numbers of the composition operator with symbol the ``cusp map'' and the lens maps, acting on weighted Dirichlet spaces.

Keywords: approximation numbers; weighted Dirichlet space; composition operator; Hardy space; Hilbert spaces of analytic functions; Schatten classes; singular numbers; weighted Bergman space

Domains: Mathematics [math]; Functional Analysis [math.FA]

Hervé Queffélec, Pascal Lefèvre, Daniel Li, Luis Rodriguez-Piazza. Comparison of singular numbers of composition operators on different Hilbert spaces of analytic functions. 2020. ⟨hal-02437146⟩