On Cesàro Operators: Boundedness, Compactness and Spectra

Abstract

The main purpose of the paper is to investigate the spectra of the Cesàro operator Cq , where on Banach spaces. For the method of the proof is to exhibit a relationship between the operator Cq and a generalized difference operator Δ ab . Furthermore, for it is shown that the operator Cq is compact on certain Banach spaces. In this case, the spectra of Cq are completely determined.