On the Spectrum of Some Infinite Matrix as an Operator on the Sequence Space c\(_0\)

In various papers some authors have previously investigated (Brown et al. 1965; Wenger 1975; Deddens 1978; Rhoads 1983; Reade 1985) and determined the spectrum of weighted mean matrices considered as bounded operators on various sequence spaces. In this study, we determine the spectrum of a Norlund matrix as a bounded operator over the sequence space c0. This will be achieved by applying spectral theory, Banach space theorems of functional analysis as well as summability methods of summability theory. In which case it is shown that the spectrum of A \(∈\) B (c0), that is \(σ\)(A) = {\(λ\) \(∈\) \(C\): |\(λ\) + 1|\(≤\) 2}. Also it is shown that (A*) = {\(λ\) \(∈\) \(C\): |\(λ\) + 1|\(≤\) 2}