One-dimensional perturbations of unbounded selfadjoint operators with empty spectrum
Spectral Theory
2013-04-23 v1 Complex Variables
Functional Analysis
Abstract
We study spectral properties of one-dimensional singular perturbations of an unbounded selfadjoint operator and give criteria for the possibility to remove the whole spectrum by a perturbation of this type. A counterpart of our results for the case of bounded operators provides a complete description of compact selfadjoint operators whose rank one perturbation is a Volterra operator.
Cite
@article{arxiv.1304.5800,
title = {One-dimensional perturbations of unbounded selfadjoint operators with empty spectrum},
author = {Anton D. Baranov and Dmitry V. Yakubovich},
journal= {arXiv preprint arXiv:1304.5800},
year = {2013}
}
Comments
20 pages. Part of these results was announced in arXiv:1212.6014