Spectral properties of weighted composition semigroups on the Bloch space

Abstract

We determine both the semigroup and spectral properties of a group of weighted SBS composition operators on the Little Bloch space. It turns out that these are strongly continuous groups of invertible isometries on the Bloch space. We then obtain the norm and spectra of the infinitesimal generator as well as the resulting resolvents which are given as integral operators. Using the spectral mapping theorem as well as the Hille Yosida theorem we obtain the spectral properties of the resulting integral operators.