Rotations of eigenvectors under unbounded perturbations
Michael Gil'
Ben Gurion University, Beer Sheva, Israel
![Rotations of eigenvectors under unbounded perturbations cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jst-volume-7-issue-1.png&w=3840&q=90)
Abstract
Let be an unbounded selfadjoint positive definite operator with a discrete spectrum in a separable Hilbert space, and be a linear operator, such that . It is assumed that has a simple eigenvalue. Under certain conditions also has a simple eigenvalue. We derive an estimate for , where and are the normalized eigenvectors corresponding to these simple eigenvalues of and , respectively. Besides, the perturbed operator can be non-selfadjoint. To illustrate that estimate we consider a non-selfadjoint differential operator. Our results can be applied in the case when is a normal operator.
Cite this article
Michael Gil', Rotations of eigenvectors under unbounded perturbations. J. Spectr. Theory 7 (2017), no. 1, pp. 191–199
DOI 10.4171/JST/159