Open Access

# A spectral decomposition in one class of non-selfadjoint operators

### Abstract

In this paper, a class of special finite dimensional perturbations of Volterra operators in Hilbert spaces is investigated. The main result of the article is finding necessary and sufficient conditions for an operator in a chosen class to be similar to the orthogonal sum of a dissipative and an anti-dissipative operators with finite dimensional imaginary parts.

### Article Information

 Title A spectral decomposition in one class of non-selfadjoint operators Source Methods Funct. Anal. Topology, Vol. 16 (2010), no. 2, 140-157 MathSciNet MR2667809 Copyright The Author(s) 2010 (CC BY-SA)

### Authors Information

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

M. V. Dolgopolova
Poltava National Technical University, 24 Pervomaiskii prospect, Poltava, 36011, Ukraine

S. I. Nedobachiy
Poltava National Technical University, 24 Pervomaiskii prospect, Poltava, 36011, Ukraine

### Citation Example

G. M. Gubreev, M. V. Dolgopolova, and S. I. Nedobachiy, A spectral decomposition in one class of non-selfadjoint operators, Methods Funct. Anal. Topology 16 (2010), no. 2, 140-157.

### BibTex

@article {MFAT532,
AUTHOR = {Gubreev, G. M. and Dolgopolova, M. V. and Nedobachiy, S. I.},
TITLE = {A spectral decomposition in one class of non-selfadjoint operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {16},
YEAR = {2010},
NUMBER = {2},
PAGES = {140-157},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=532},
}