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Spectral properties of weighted composition operators on the Bloch and Dirichlet spaces

Volume 232 / 2016

Ted Eklund, Mikael Lindström, Paweł Mleczko Studia Mathematica 232 (2016), 95-112 MSC: Primary 47B33; Secondary 47B38. DOI: 10.4064/sm8310-3-2016 Published online: 21 April 2016

Abstract

The spectra of invertible weighted composition operators $uC_\varphi $ on the Bloch and Dirichlet spaces are studied. In the Bloch case we obtain a complete description of the spectrum when $\varphi $ is a parabolic or elliptic automorphism of the unit disc. In the case of a hyperbolic automorphism $\varphi $, exact expressions for the spectral radii of invertible weighted composition operators acting on the Bloch and Dirichlet spaces are derived.

Authors

  • Ted EklundDepartment of Mathematics
    Åbo Akademi University
    FI-20500 Åbo, Finland
    e-mail
  • Mikael LindströmDepartment of Mathematics
    Åbo Akademi University
    FI-20500 Åbo, Finland
    e-mail
  • Paweł MleczkoFaculty of Mathematics and Computer Science
    Adam Mickiewicz University
    Umultowska 87
    61-614 Poznań, Poland
    e-mail

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