Spectral properties of weighted composition operators on the Bloch and Dirichlet spaces
Volume 232 / 2016
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.
