We characterize the spectrum and essential spectrum of “essentially linear fractional” composition operators acting on the Hardy space H2(U) of the open unit disc U. When the symbols of these composition operators have Denjoy-Wolff point on the unit circle, the spectrum and essential spectrum coincide. Our work permits us to describe the spectrum and essential spectrum of certain associated wei...

We study when weighted composition operators Cφ,ψ acting between weighted Bergman spaces of infinite order are power bounded resp. uniformly mean ergodic.

We investigate weighted composition operators that attain their norm on weighted Banach spaces of holomorphic functions on the unit disc of type H∞. Applications for composition operators on weighted Bloch spaces are given.

We consider differences of weighted composition operators between given weighted Bergman spaces H∞ v of infinite order and characterize boundedness and the essential norm of these differences.