On the spectrum of a special Nörlund matrix as an operator on c0

Abstract

In summability theory, different classes of matrices have been investigated and characterized. There are various types of summability methods e.g. Nörlund means, Cesaro, Riesz, Euler, Abel and many others. The spectrum of an operator plays a crucial role in the development of Tauberian theory for the operator and Mercerian theorems which are used to determine the limit or sum of a convergent sequence or series. In this paper, the spectrum and eigenvalues of a special Nörlund matrix as a bounded operator on the sequence space c0 is investigated. This is achieved by applying Banach space theorems of functional analysis as well as summability methods of summability theory.