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Completeness of rank one perturbations of normal operators with lacunary spectrum. / Baranov, A. D.; Yakubovich, D. V.

In: Journal of Spectral Theory, Vol. 8, No. 1, 01.01.2018, p. 1-32.

Research output: Contribution to journal › Article › peer-review

Harvard

Baranov, AD & Yakubovich, DV 2018, 'Completeness of rank one perturbations of normal operators with lacunary spectrum', Journal of Spectral Theory, vol. 8, no. 1, pp. 1-32. https://doi.org/10.4171/JST/190

APA

Baranov, A. D., & Yakubovich, D. V. (2018). Completeness of rank one perturbations of normal operators with lacunary spectrum. Journal of Spectral Theory, 8(1), 1-32. https://doi.org/10.4171/JST/190

Vancouver

Baranov AD, Yakubovich DV. Completeness of rank one perturbations of normal operators with lacunary spectrum. Journal of Spectral Theory. 2018 Jan 1;8(1):1-32. https://doi.org/10.4171/JST/190

Author

Baranov, A. D. ; Yakubovich, D. V. / Completeness of rank one perturbations of normal operators with lacunary spectrum. In: Journal of Spectral Theory. 2018 ; Vol. 8, No. 1. pp. 1-32.

BibTeX

@article{3c65083c33ec4dc0abcc8d1c5e2da3e8,
title = "Completeness of rank one perturbations of normal operators with lacunary spectrum",
abstract = "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.",
keywords = "Completeness of eigenvectors, P{\'o}lya peaks, Rank one perturbation, Selfadjoint operator",
author = "Baranov, {A. D.} and Yakubovich, {D. V.}",
year = "2018",
month = jan,
day = "1",
doi = "10.4171/JST/190",
language = "English",
volume = "8",
pages = "1--32",
journal = "Journal of Spectral Theory",
issn = "1664-039X",
publisher = "European Mathematical Society Publishing House",
number = "1",

}

RIS

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 -

ID: 32722574