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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 2, Pages 350–361
DOI: https://doi.org/10.33048/smzh.2023.64.209 (Mi smj7766) 		 
Spectral properties of strongly bounded operators

E. V. Mel'nikov

Omsk State University
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DOI: https://doi.org/10.33048/smzh.2023.64.209
Abstract: We show that strongly bounded operators in locally convex spaces and topological vector spaces under some additional conditions have the spectral properties similar to those of bounded operators in normed spaces. Such operator enjoys the Berling–Gelfand formula in a sequentially complete locally convex space.
Keywords: topological vector spaces, locally convex spaces, strongly bounded operators, resolvent, spectrum, spectral radius.
Received: 27.02.2022
Revised: 27.06.2022
Accepted: 15.08.2022
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 2, Pages 347–355
DOI: https://doi.org/10.1134/S003744662302009X
Document Type: Article
UDC: 517.983:517.986
Language: Russian
Citation: E. V. Mel'nikov, “Spectral properties of strongly bounded operators”, Sibirsk. Mat. Zh., 64:2 (2023), 350–361; Siberian Math. J., 64:2 (2023), 347–355
Citation in format AMSBIB
\Bibitem{Mel23}
\by E.~V.~Mel'nikov
\paper Spectral properties of strongly bounded operators
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 2
\pages 350--361
\mathnet{http://mi.mathnet.ru/smj7766}
\crossref{https://doi.org/10.33048/smzh.2023.64.209}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 2
\pages 347--355
\crossref{https://doi.org/10.1134/S003744662302009X}
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    		Сибирский математический журнал Siberian Mathematical Journal
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