Geodesic
Spectral properties of weighted composition operators on the Bloch and Dirichlet spaces
Ted Eklund 1   ; Mikael Lindström 1   ; Paweł Mleczko 2
1 Department of Mathematics Åbo Akademi University FI-20500 Åbo, Finland
2 Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87 61-614 Poznań, Poland
Studia Mathematica, Tome 232 (2016) no. 2, pp. 95-112 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm8310-3-2016
Keywords: spectra invertible weighted composition operators varphi bloch dirichlet spaces studied bloch obtain complete description spectrum varphi parabolic elliptic automorphism unit disc hyperbolic automorphism varphi exact expressions spectral radii invertible weighted composition operators acting bloch dirichlet spaces derived

Ted Eklund  1   ; Mikael Lindström  1   ; Paweł Mleczko  2

1 Department of Mathematics Åbo Akademi University FI-20500 Åbo, Finland
2 Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87 61-614 Poznań, Poland 
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     title = {Spectral properties of weighted composition operators on the {Bloch} and {Dirichlet} spaces},
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Ted Eklund; Mikael Lindström; Paweł Mleczko. Spectral properties of weighted composition operators on the Bloch and Dirichlet spaces. Studia Mathematica, Tome 232 (2016) no. 2, pp. 95-112. doi: 10.4064/sm8310-3-2016

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