Fine spectra of the discrete generalized Cesàro operator on Banach sequence spaces

This paper concerns the spectrum and the fine spectrum of the discrete generalized
Cesàro operator Ct , where 0 ≤ t < 1, on Banach sequence spaces close to l1 and 
∞l.
We derive some compactness results for the operator Ct to describe the spectrum. Our
technique involves standard operator theory and summability theory.