Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2024, Volume 235, Pages 3–14
DOI: https://doi.org/10.36535/2782-4438-2024-235-3-14 (Mi into1304) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On equivalent operators

A. G. Baskakova, G. V. Garkavenkoa, N. B. Uskovab, L. N. Kostinaa

a Voronezh State University
b Voronezh State Technical University
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DOI: https://doi.org/10.36535/2782-4438-2024-235-3-14
Abstract: In this paper, we introduce the concept of equivalent operators, i.e., operators with the same invertibility states, and establish their connection with weakly similar and similar operators. We find the invertibility states of some classes of linear operators, in particular, operators with involution and operators with compact resolvent. We discuss approaches to constructing equivalent operators and give examples of equivalent operators.
Keywords: invertibility states, equivalent operators, strongly equivalent operators, weakly similar operators, similar operators
Document Type: Article
UDC: 517.9
MSC: 47A99, 47B01
Language: Russian
Citation: A. G. Baskakov, G. V. Garkavenko, N. B. Uskova, L. N. Kostina, “On equivalent operators”, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 235, VINITI, Moscow, 2024, 3–14
Citation in format AMSBIB
\Bibitem{BasGarUsk24}
\by A.~G.~Baskakov, G.~V.~Garkavenko, N.~B.~Uskova, L.~N.~Kostina
\paper On equivalent operators
\inbook Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2024
\vol 235
\pages 3--14
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1304}
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