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The Spectrum of a Composition Operator and Calderón’s Complex Interpolation

  • Matthew A. Pons
Part of the Operator Theory: Advances and Applications book series (OT, volume 202)

Abstract

Using the method of complex interpolation due to A.P. Calderón, we give a general theorem for identifying the spectrum of an operator acting on a family of interpolation spaces. We then use this to determine the spectrum of certain composition operators acting on the weighted Dirichlet and analytic Besov spaces of the unit disk.

Keywords

Composition operators complex interpolation spectra 

Mathematics Subject Classification (2000)

Primary 46B70 47B33 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Matthew A. Pons
    • 1
  1. 1.Department of MathematicsNorth Central CollegeNapervilleUSA

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