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

Abstract

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

17 pages