# Approximation numbers of weighted composition operators

Abstract : We study the approximation numbers of weighted composition operators $f\mapsto w\cdot(f\circ\varphi)$ on the Hardy space $H^2$ on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers are derived. For the special class of weighted lens map composition operators with specific weights, we show how much the weight $w$ can improve the decay rate of the approximation numbers, and give sharp upper and lower bounds. These examples are motivated from applications to the analysis of relative commutants of special inclusions of von Neumann algebras appearing in quantum field theory (Borchers triples).
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https://hal-univ-artois.archives-ouvertes.fr/hal-01410297
Contributor : Daniel Li <>
Submitted on : Tuesday, December 6, 2016 - 3:40:14 PM
Last modification on : Thursday, September 27, 2018 - 2:58:02 PM

### Identifiers

• HAL Id : hal-01410297, version 1
• ARXIV : 1612.01177

### Citation

Gandalf Lechner,, Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza. Approximation numbers of weighted composition operators . 2016. ⟨hal-01410297⟩

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