Year: 2019
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Wahl, Martin
Institution: Humboldt-Universität zu Berlin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2980995152