SPECTRUM AND COMPACTNESS OF THE CESÀRO OPERATOR ON WEIGHTED $\ell_p$ SPACES

An investigation is made of the continuity, the compactness and the spectrum of the Cesàro operator $C$ when acting on the weighted Banach sequence spaces $\ell_p(w)$, $1<p<\infty$, for a positive, decreasing weight $w$, thereby extending known results for $C$ when acting on the classical spaces $\ell_p$. New features arise in the weighted setting (e.g., existence of eigenvalues, compactness) which are not present in $\ell_p$