Spectral properties of generalized Cesàro operators on Hardy and weighted Bergman spaces

We investigate spectral properties of integral operators of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{g} f(z) = \frac{1}{z}\int\limits_0^z f(\omega )g(\omega )d\omega $$\end{document} acting on Banach spaces of analytic functions on the unit disc. In the case that g is a rational function, analytic on the unit disc, we obtain the spectrum, essential spectrum and index of Sg. Finally, we give examples of such operators pertaining to hyponormality.