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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 204, Pages 3–15
DOI: https://doi.org/10.36535/0233-6723-2022-204-3-15 (Mi into936) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Method of similar operators in the problem of bi-invariant subspaces

A. G. Baskakovab, G. V. Garkavenkoc, I. A. Krishtald, N. B. Uskovae

a North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz
b Voronezh State University
c Voronezh State Pedagogical University
d Northern Illinois University
e Voronezh State Technical University
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DOI: https://doi.org/10.36535/0233-6723-2022-204-3-15
Abstract: In this paper, we discuss the construction of bi-invariant subspaces for a self-adjoint, linear, closed operator with discrete spectrum perturbed by a bounded operator. The main result is the theorem on the similarity of this operator to a block diagonal operator. This theorem implies results concerning biinvariant subspaces and formulas for projectors and weighted average eigenvalues. In addition, we construct the corresponding group of operators and propose a new modification of the method of similar operators.
Keywords: method of similar operators, spectral projectors, biinvariant subspaces.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00732
This work was supported by the Russian Foundation for Basic Research (project No. 19-01-00732).
Document Type: Article
UDC: 517.9
MSC: 47A75, 47B25, 47B36
Language: Russian
Citation: A. G. Baskakov, G. V. Garkavenko, I. A. Krishtal, N. B. Uskova, “Method of similar operators in the problem of bi-invariant subspaces”, Proceedings of the Voronezh spring mathematical school  "Modern methods of the theory of boundary-value problems. Pontryagin  readings – XXXI". Voronezh, May 3-9, 2020, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 204, VINITI, Moscow, 2022, 3–15
Citation in format AMSBIB
\Bibitem{BasGarKri22}
\by A.~G.~Baskakov, G.~V.~Garkavenko, I.~A.~Krishtal, N.~B.~Uskova
\paper Method of similar operators in the problem of bi-invariant subspaces
\inbook Proceedings of the Voronezh spring mathematical school 
"Modern methods of the theory of boundary-value problems. Pontryagin  readings – XXXI".
Voronezh, May 3-9, 2020
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 204
\pages 3--15
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into936}
\crossref{https://doi.org/10.36535/0233-6723-2022-204-3-15}
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    • This publication is cited in the following 1 articles:
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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