TY - JOUR

T1 - Completeness of rank one perturbations of normal operators with lacunary spectrum

AU - Baranov, A. D.

AU - Yakubovich, D. V.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Suppose A is a compact normal operator on a Hilbert space H with certain lacunarity condition on the spectrum (which means, in particular, that its eigenvalues go to zero exponentially fast), and let L be its rank one perturbation. We show that either infinitely many moment equalities hold or the linear span of root vectors of L, corresponding to non-zero eigenvalues, is of finite codimension in H. In contrast to classical results, we do not assume the perturbation to be weak.

AB - Suppose A is a compact normal operator on a Hilbert space H with certain lacunarity condition on the spectrum (which means, in particular, that its eigenvalues go to zero exponentially fast), and let L be its rank one perturbation. We show that either infinitely many moment equalities hold or the linear span of root vectors of L, corresponding to non-zero eigenvalues, is of finite codimension in H. In contrast to classical results, we do not assume the perturbation to be weak.

KW - Completeness of eigenvectors

KW - Pólya peaks

KW - Rank one perturbation

KW - Selfadjoint operator

UR - http://www.scopus.com/inward/record.url?scp=85042744815&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/completeness-rank-one-perturbations-normal-operators-lacunary-spectrum

U2 - 10.4171/JST/190

DO - 10.4171/JST/190

M3 - Article

AN - SCOPUS:85042744815

VL - 8

SP - 1

EP - 32

JO - Journal of Spectral Theory

JF - Journal of Spectral Theory

SN - 1664-039X

IS - 1

ER -