Rotations of eigenvectors under unbounded perturbations

  • Michael Gil'

    Ben Gurion University, Beer Sheva, Israel

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