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Approximation numbers of weighted composition operators

Lechner, Gandalf, Li, Daniel, Queffélec, Hervé and Rodriguez-Piazza, Luis 2018. Approximation numbers of weighted composition operators. Journal of Functional Analysis 274 (7) , pp. 1928-1958. 10.1016/j.jfa.2018.01.010

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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).

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Elsevier
ISSN: 0022-1236
Date of First Compliant Deposit: 22 January 2018
Date of Acceptance: 22 January 2018
Last Modified: 02 Jul 2019 07:27
URI: http://orca.cf.ac.uk/id/eprint/108334

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