THE SPECTRAL ANALYSIS OF NEWLY DEFINED NORLUND MATRICES: THE EIGENVALUES AS AN OPERATOR ON (C) AND (C_0) SPACES

This paper investigates the spectral analysis of newly defined Norlund infinite matrix: the eigenvalues as an operator on the sequence spaces \(c_0\) and \(c\). The newly defined Norlund matrix, a conception of Cesaro matrix, has been greatly studied in the context of summability theory. However, its spectral analysis on the sequence space \(c_0\) and \(c\) stay mostly undiscovered. This paper explored and presented the spectral analysis of newly defined Norlund Infinite matrix: the eigenvalues of a Norlund Infinite matrix as an operator on the sequence space \(c_0\) and \(c\). Through the eigenvalue problem \(Zx=\lambda x\). The findings at the end of the research are \(Z\in B(c_0)\) has no eigenvalues and \(Z\in B(c)\) has the set 1 and their spectra presented.