The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions

For a wide class of radial weights we calculate the essential norm of a weighted composition operator on the weighted Banach spaces of analytic functions in terms of the analytic function and the n th power of the analytic selfmap of the open unit disc . We also apply our result to calculate the ess...

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Bibliographic Details
Published in:Integral equations and operator theory 2012-02, Vol.72 (2), p.151-157
Main Authors: Hyvärinen, Olli, Kemppainen, Mika, Lindström, Mikael, Rautio, Antti, Saukko, Erno
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:For a wide class of radial weights we calculate the essential norm of a weighted composition operator on the weighted Banach spaces of analytic functions in terms of the analytic function and the n th power of the analytic selfmap of the open unit disc . We also apply our result to calculate the essential norm of composition operators acting on Bloch type spaces with general radial weights.
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-011-1919-7