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Matematicheskie Zametki, 2023, Volume 114, Issue 5, Pages 780–788
DOI: https://doi.org/10.4213/mzm13982 (Mi mzm13982) 		 
On the Existence of an Element with Given Deviations from an Expanding System of Subspaces

Yu. A. Skvortsovab

a Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics
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DOI: https://doi.org/10.4213/mzm13982
Abstract: We expand the class of deviation sequences for which the problem on the existence of an element of a Banach space with these deviations from a system of nested subspaces is solved positively regardless of the space and the system of subspaces. This result is used to narrow the gap between the weak asymptotics constants in S. V. Konyagin's theorem on the existence of an element whose deviations are asymptotically close to given ones.
Keywords: Banach space, subspace, deviations, Bernstein problem.
Funding agency Grant number
Russian Science Foundation 23-71-30001
This work was financially supported by the Russian Science Foundation (project 23-71-30001, https://rscf.ru/en/project/23-71-30001/) at Lomonosov Moscow State University.
Received: 15.04.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 5, Pages 949–956
DOI: https://doi.org/10.1134/S0001434623110299
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
MSC: 46B20
Language: Russian
Citation: Yu. A. Skvortsov, “On the Existence of an Element with Given Deviations from an Expanding System of Subspaces”, Mat. Zametki, 114:5 (2023), 780–788; Math. Notes, 114:5 (2023), 949–956
Citation in format AMSBIB
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\paper On the Existence of an Element with Given Deviations from an Expanding System of Subspaces
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\yr 2023
\vol 114
\issue 5
\pages 780--788
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\crossref{https://doi.org/10.4213/mzm13982}
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\transl
\jour Math. Notes
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\vol 114
\issue 5
\pages 949--956
\crossref{https://doi.org/10.1134/S0001434623110299}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85187712640}
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