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. © 2020, Springer-Verlag GmbH Austria, part of Springer Nature.