Generalized Cesàro operators in weighted Banach spaces of analytic functions with sup-norms

Kurzfassung/Abstract

An investigation is made of the generalized Cesàro operators Ct, for t ∈ [0, 1], when they act on the space H(D) of holomorphic functions on the open unit disc D, on the Banach space H∞ of bounded analytic functions and on the weighted Banach spaces H∞
v and H0 v with their sup-norms. Of particular interest are the continuity, compactness, spectrum and point spectrum of Ct as well as their linear dynamics and mean ergodicity.