Spectral properties of perturbed linear operators and their application to infinite matrices
F.O. Farid · Proceedings of the American Mathematical Society · 1991
In this paper, upper bounds for the difference between the eigenvalues and the eigenvectors of a closed linear operator D D and those of D + F D + F , where F F is a bounded linear operator, are given in terms of the norm of F F . These results are applied to approximate the eigenvalues and the eigenvectors of a diagonally infinite matrix by those of its corresponding diagonal matrix.