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

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