Research output: Contribution to journal › Article › peer-review
Spectral theory of rank one perturbations of normal compact operators. / Baranov, A. D.
In: St. Petersburg Mathematical Journal, Vol. 30, No. 5, 01.01.2019, p. 761-802.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 51700667