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

Abstract

An investigation is made of the generalized Cesàro operators \(C_t\) , for \(t\in [0,1]\) , when they act on the space \(H({{\mathbb {D}}})\) of holomorphic functions on the open unit disc \({{\mathbb {D}}}\) , 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.