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

Abstract 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.