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Composition operators on weighted Bergman spaces of a half-plane

Part of: Special classes of linear operators

Published online by Cambridge University Press:  25 February 2011

Sam J. Elliott  and
Andrew Wynn
Sam J. Elliott
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, UK, (samuel@maths.leeds.ac.uk)
Andrew Wynn
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK, (andrew.wynn@ucl.ac.uk)
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Abstract

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We use induction and interpolation techniques to prove that a composition operator induced by a map ϕ is bounded on the weighted Bergman space of the right half-plane if and only if ϕ fixes the point at ∞ non-tangentially and if it has a finite angular derivative λ there. We further prove that in this case the norm, the essential norm and the spectral radius of the operator are all equal and are given by λ(2+α)/2.

Keywords

composition operatorweighted Bergman spaceinterpolation

MSC classification

Secondary: 47B33: Composition operators
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 2 , June 2011 , pp. 373 - 379
Copyright
Copyright © Edinburgh Mathematical Society 2011

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