The spectrum and some subdivisions of the spectrum of the generalized αq-Cesàro operators on ℓp (1 < p < ∞)

Abstract

Recently, the spectrum of the q-Cesàro matrix, which is considered an operator on [Formula: see text], [Formula: see text] and [Formula: see text], and its various spectral competitions have been determined by Yildirim, Durna–Turkay and El-Shabrawy, respectively. Later, Türkay determined the spectral decompositions of the generalized [Formula: see text]-Cesàro operators on [Formula: see text] and [Formula: see text], giving this matrix in its special case. This paper examines the spectra and fine spectra of the generalized [Formula: see text]-Cesàro operators on [Formula: see text], taking the result of El-Shabrawy as a special case.