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Approximation numbers of weighted composition operators


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Author: Lechner, Gandalf
Li, Daniel
Queffélec, Hervé
Rodríguez Piazza, Luis
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2018
Published in: Journal of Functional Analysis
Document type: Article
Abstract: We study the approximation numbers of weighted composition operators f 7→ w · (f ◦ ϕ) on the Hardy space H2 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).
Cite: Lechner, G., Li, D., Queffélec, H. y Rodríguez Piazza, L. (2018). Approximation numbers of weighted composition operators. Journal of Functional Analysis
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DOI: 10.1016/j.jfa.2018.01.010

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