Approximation numbers of weighted composition operators |
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Authors: | G Lechner D Li H Queffélec L Rodríguez-Piazza |
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Institution: | 1. Cardiff University, School of Mathematics, UK;2. Université d''Artois, Laboratoire de Mathématiques de Lens (LML), France;3. Université Lille Nord de France, France;4. Universidad de Sevilla, Spain |
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Abstract: | We study the approximation numbers of weighted composition operators on the Hardy space 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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Keywords: | Composition operators Approximation numbers von Neumann algebras |
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