Some Spectrum Estimates of the $ \alpha q$-Cesaro Matrices with $0<\alpha ,q<1$ on $c_{0}$

Abstract

The main purpose of the this paper is to investigate the spectrum, the fine spectrum, the approximate point spectrum, the defect spectrum, and the compression spectrum of the genaralized $\alpha q$-Ces\`{a}ro matrix $% C_{q}^{\alpha }$ with $\alpha ,q\in \left( 0,1\right) $ on the sequence space $c_{0}$.