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# Approximation numbers of weighted composition operators

 Lechner, G., Li, D., Queffélec, H. and Rodriguez-Piazza, L. 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 Publication Published Mathematics Q Science > QA Mathematics Elsevier 0022-1236 22 January 2018 19 January 2018 24 Nov 2020 23:02 http://orca-mwe.cf.ac.uk/id/eprint/108334

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