TY - JOUR

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

AU - Baranov, A. D.

N1 - A. D. Baranov, “Spectral theory of rank one perturbations of normal compact operators”, Алгебра и анализ, 30:5 (2018), 1–56; St. Petersburg Math. J., 30:5 (2019), 761–802

PY - 2018/10/1

Y1 - 2018/10/1

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 - Spectral synthesis

KW - nonvanishing moments

KW - Domination

KW - Completeness

KW - Spectrum

KW - Invariant subspace

KW - functional model

UR - https://www.elibrary.ru/item.asp?id=35659876

M3 - Article

VL - 30

SP - 1

EP - 56

JO - АЛГЕБРА И АНАЛИЗ

JF - АЛГЕБРА И АНАЛИЗ

SN - 0234-0852

IS - 5

ER -