On the Eigenvalues of a Norlund Infinite Matrix as an Operator on Some Sequence Spaces

Abstract

In various papers some authors have previously investigated [1], [2], [3], [4], [5] and determined the spectrum of weighted mean matrices considered as bounded operators on various sequence spaces. In this study, we determine eigen values of a Norlund matrix as a bounded operator over the sequence space . This will be achieved by applying Banach space theorems of functional analysis as well as summability methods of summability theory. We are also going to apply eigenvalue problem i.e. Ax= λ x. Where λ are numbers (realorcomplex) and vector columns ;such that . In which case it is shown that the set of Eigen values of {λ∈C:|λ+1|<2}∪{1}