Generalized Cesàro operators in the disc algebra and in Hardy spaces

Abstract

Generalized Cesàro operators \(C_t\), for \(t\in [0,1)\), are investigated when they act on the disc algebra \(A({\mathbb {D}})\) and on the Hardy spaces \(H^p\), for \(1\le p \le \infty \). We study the continuity, compactness, spectrum and point spectrum of \(C_t\) as well as their linear dynamics and mean ergodicity on these spaces.