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Eurasian Mathematical Journal, 2020, Volume 11, Number 2, Pages 65–71
DOI: https://doi.org/10.32523/2077-9879-2020-11-2-65-71 (Mi emj366) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On stability of bases in Hilbert spaces

E. A. Larionov

Department of Applied Mathematics, Moscow State University of Civil Engineering, 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation
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DOI: https://doi.org/10.32523/2077-9879-2020-11-2-65-71
Abstract: In a Hilbert space we consider a minimal and complete system asymptotically close to an almost normed unconditional basis and find conditions under which such system also forms an unconditional basis. The proof of this statement is based on a new criterion of compactness of linear operators proposed in this paper.
Keywords and phrases: perturbation, compact operator, orthoprojector, isotropically non-compact sequence.
Received: 29.06.2019
Bibliographic databases:
Document Type: Article
MSC: 35P15
Language: English
Citation: E. A. Larionov, “On stability of bases in Hilbert spaces”, Eurasian Math. J., 11:2 (2020), 65–71
Citation in format AMSBIB
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\paper On stability of bases in Hilbert spaces
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