2000 character limit reached
One-dimensional perturbations of unbounded selfadjoint operators with empty spectrum (1304.5800v1)
Published 21 Apr 2013 in math.SP, math.CV, and math.FA
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.