The Cesàro Operator on Duals of Smooth Sequence Spaces of Infinite Type

The discrete Cesàro operator C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {C}$$\end{document} is investigated in strong duals of smooth sequence spaces of infinite type. Of main interest is its spectrum, which turns out to be distinctly different in the cases when the space is nuclear and when it is not.