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Regular version of the site

Article

One-dimensional perturbations of unbounded selfadjoint operators with empty spectrum

Journal of Mathematical Analysis and Applications. 2015. Vol. 424. No. 2. P. 1404-1424.
Baranov A., Yakubovich D.

We study spectral properties of one-dimensional singular nonselfadjoint 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.