TY - JOUR

T1 - Spectral theory of rank one perturbations of normal compact operators

AU - Baranov, A. D.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - A functional model is constructed for rank one perturbations of compact normal operators that act in a certain Hilbert spaces of entire functions generalizing the de Branges spaces. By using this model, completeness and spectral synthesis problems are studied for such perturbations. Previously, the spectral theory of rank one perturbations was developed in the selfadjoint case by D. Yakubovich and the author. In the present paper, most of known results in the area are extended and simplified significantly. Also, an ordering theorem for invariant subspaces with common spectral part is proved. This result is new even for rank one perturbations of compact selfadjoint operators.

AB - A functional model is constructed for rank one perturbations of compact normal operators that act in a certain Hilbert spaces of entire functions generalizing the de Branges spaces. By using this model, completeness and spectral synthesis problems are studied for such perturbations. Previously, the spectral theory of rank one perturbations was developed in the selfadjoint case by D. Yakubovich and the author. In the present paper, most of known results in the area are extended and simplified significantly. Also, an ordering theorem for invariant subspaces with common spectral part is proved. This result is new even for rank one perturbations of compact selfadjoint operators.

KW - Completeness

KW - Domination

KW - Functional model

KW - Invariant subspace

KW - Nonvanishing moments

KW - Spectral synthesis

KW - Spectrum

UR - http://www.scopus.com/inward/record.url?scp=85070095904&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=41622974

U2 - 10.1090/spmj/1569

DO - 10.1090/spmj/1569

M3 - Article

AN - SCOPUS:85070095904

VL - 30

SP - 761

EP - 802

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 5

ER -