Integral Equations and Operator Theory

, Volume 72, Issue 2, pp 151–157 | Cite as

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

  • Olli Hyvärinen
  • Mika Kemppainen
  • Mikael Lindström
  • Antti Rautio
  • Erno Saukko
Article

Abstract

For a wide class of radial weights we calculate the essential norm of a weighted composition operator \({uC_\varphi}\) on the weighted Banach spaces of analytic functions in terms of the analytic function \({u \colon \mathbb D \to \mathbb C}\) and the nth power of the analytic selfmap \({\varphi}\) of the open unit disc \({\mathbb D}\) . We also apply our result to calculate the essential norm of composition operators acting on Bloch type spaces with general radial weights.

Mathematics Subject Classification (2010)

Primary 47B33 47B38 

Keywords

Essential norm weighted composition operator 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Olli Hyvärinen
    • 1
  • Mika Kemppainen
    • 1
  • Mikael Lindström
    • 1
  • Antti Rautio
    • 1
  • Erno Saukko
    • 1
  1. 1.Department of Mathematical SciencesUniversity of OuluOuluFinland

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