Spectral Properties of Perturbed Linear Operators and their Application to Infinite Matrices
- 1 August 1991
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 112 (4) , 1013-1022
- https://doi.org/10.2307/2048648
Abstract
In this paper, upper bounds for the difference between the eigenvalues and the eigenvectors of a closed linear operator and those of , where is a bounded linear operator, are given in terms of the norm of . These results are applied to approximate the eigenvalues and the eigenvectors of a diagonally infinite matrix by those of its corresponding diagonal matrix.Keywords
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