Mean ergodic properties of the continuous Cesàro operators

Abstract

Various properties of the (continuous) Cesàro operator $\mathsf{C}$, acting on Banach and Fréchet spaces of continuous functions and $L^p$-spaces, are investigated. For instance, the spectrum and point spectrum of $\mathsf{C}$ are completely determined and a study of certain dynamics of $\mathsf{C}$ is undertaken (eg. hyper- and supercyclicity, chaotic behaviour). In addition, the mean (and uniform mean) ergodic nature of $\mathsf{C}$ acting in the various spaces is identified.

arXiv comment19 pages