Spectral theory of rank one perturbations of normal compact operators

Baranov, A.

doi:10.1090/spmj/1569

Spectral theory of rank one perturbations of normal compact operators
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by A. D. Baranov

St. Petersburg Math. J. 30 (2019), 761-802

DOI: https://doi.org/10.1090/spmj/1569

Published electronically: July 26, 2019

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Abstract:

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.

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