Mean ergodicity and spectrum of the Cesàro operator on weighted $c_0$ spaces

A detailed investigation is made of the continuity, the compactness and the spectrum of the Cesàro operator C acting on the weighted Banach sequence space $c_0(w)$ for a bounded, strictly positive weight $w$. New features arise in the weighted setting (e.g. existence of eigenvalues, compactness, mean ergodicity) which are not present in the classical setting of $c_0$