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arXiv · 1910.08460

On the perturbation series for eigenvalues and eigenprojections

Martin Wahl
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Abstract

A standard perturbation result states that perturbed eigenvalues and eigenprojections admit a perturbation series provided that the operator norm of the perturbation is smaller than a constant times the corresponding eigenvalue isolation distance. In this paper, we show that the same holds true under a weighted condition, where the perturbation is symmetrically normalized by the square-root of the reduced resolvent. This weighted condition originates in random perturbations where it leads to significant improvements.

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BibTeXRIS

Martin Wahl. 2019-10-18. On the perturbation series for eigenvalues and eigenprojections. https://arxiv.org/abs/1910.08460

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