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# On one class of nonselfadjoint operators with a discrete spectrum

### Abstract

In this work completely continious nondissipative operators with two-dimensional imaginary parts, acting in separable Hilbert space are studied. The criteria of completeness and unconditional basis property of root vectors of such operators are obtained. The results are formulated in terms of characteristic matrix-valued functions of nonselfadjoint operators and proved using analysis of functional models in de Branges spaces.

### Article Information

 Title On one class of nonselfadjoint operators with a discrete spectrum Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 3, 211-218 MathSciNet MR2857724 Copyright The Author(s) 2011 (CC BY-SA)

### Authors Information

G. M. Gubreev
Poltava National Technical University, 24 Pervomaiskii prospect, Poltava, 36011, Ukraine

M. G. Volkova
South Ukrainian Pedagogical University, 26 Staroportofrankivs'ka, Odesa, 65091, Ukraine

A. A. Tarasenko

### Citation Example

G. M. Gubreev, M. G. Volkova, and A. A. Tarasenko, On one class of nonselfadjoint operators with a discrete spectrum, Methods Funct. Anal. Topology 17 (2011), no. 3, 211-218.

### BibTex

@article {MFAT598,
AUTHOR = {Gubreev, G. M. and Volkova, M. G. and Tarasenko, A. A.},
TITLE = {On one class of nonselfadjoint operators with a discrete spectrum},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {3},
PAGES = {211-218},
ISSN = {1029-3531},
MRNUMBER = {MR2857724},
URL = {http://mfat.imath.kiev.ua/article/?id=598},
}