Geodesic
Spectral properties of weighted composition operators on the Bloch and Dirichlet spaces
Ted Eklund1 ; Mikael Lindström1 ; Paweł Mleczko2
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

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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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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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