On q−Cesàro Operators: Boundedness, Compactness and Spectra. (4th July 2021) - El-Shabrawy, Saad R.
Abstract: The main purpose of the paper is to investigate the spectra of the q − Cesàro operator Cq, where 0 < q < ∞, on Banach spaces. For 0 < q < 1, the method of the proof is to exhibit a relationship between the operator Cq and a generalized difference operator Δ ab . Furthermore, for 1 < q < ∞, it is shown that the operator Cq is compact on certain Banach spaces. In this case, the spectra of Cq are completely determined.