Composition operators on Besov and Dirichlet type spaces of the ball

Various operator theoretic properties of composition operators with linear fractional symbol acting on the Dirichlet space of the unit ball are discussed. Furthermore, we use Calderón’s complex interpolation to investigate the spectrum of composition operators with automorphic symbol acting on the analytic Besov spaces of the ball and on the weighted Dirichlet spaces of the ball, which include the Dirichlet, Arveson, Hardy and Bergman spaces.