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

An investigation is made of the generalized Cesàro operators Cₜ C t , for t∈ [0,1] t ∈ [ 0 , 1 ] , when they act on the space H(D) H ( D ) of holomorphic functions on the open unit disc D D , on the Banach space H^∞ H ∞ of bounded analytic functions and on the weighted Banach spaces Hᵥ^∞ H v ∞ and Hᵥ⁰ H v 0 with their sup-norms. Of particular interest are the continuity, compactness, spectrum and point spectrum of Cₜ C t as well as their linear dynamics and mean ergodicity.