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Tr. Mat. Inst. Steklova, 2014, Volume 284, Pages 212–215 (Mi tm3536)  

This article is cited in 2 scientific papers (total in 3 papers)

Deviation of elements of a Banach space from a system of subspaces

S. V. Konyagin

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

Abstract: We prove that if $X$ is a real Banach space, $Y_1\subset Y_2\subset…$ is a sequence of strictly embedded closed linear subspaces of $X$, and $d_1\ge d_2\ge…$ is a nonincreasing sequence converging to zero, then there exists an element $x\in X$ such that the distance $\rho(x,Y_n)$ from $x$ to $Y_n$ satisfies the inequalities $d_n\le\rho(x,Y_n)\le8d_n$ for $n=1,2,…$.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00329
Ministry of Education and Science of the Russian Federation NSh-6003.2012.1
This work was supported by the Russian Foundation for Basic Research (project no. 11-01-00329) and by a grant of the President of the Russian Federation (project no. NSh-6003.2012.1).


DOI: https://doi.org/10.1134/S0371968514010142

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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 284, 204–207

Bibliographic databases:

Document Type: Article
UDC: 517.982.256
Received in May 2013

Citation: S. V. Konyagin, “Deviation of elements of a Banach space from a system of subspaces”, Function spaces and related problems of analysis, Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 284, MAIK Nauka/Interperiodica, Moscow, 2014, 212–215; Proc. Steklov Inst. Math., 284 (2014), 204–207

Citation in format AMSBIB
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\by S.~V.~Konyagin
\paper Deviation of elements of a~Banach space from a~system of subspaces
\inbook Function spaces and related problems of analysis
\bookinfo Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2014
\vol 284
\pages 212--215
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968514010142}
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    This publication is cited in the following articles:
    1. A. G. Aksoy, G. Lewicki, “_orig bernstein's lethargy theorem in frechet spaces”, J. Approx. Theory, 209 (2016), 58–77  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. G. Aksoy, M. Al-Ansari, C. Case, Q. Peng, “Subspace condition for Bernstein's lethargy theorem”, Turk. J. Math., 41:5 (2017), 1101–1107  crossref  mathscinet  isi  scopus
    3. B. S. Kashin, Yu. V. Malykhin, V. Yu. Protasov, K. S. Ryutin, I. D. Shkredov, “Sergei Vladimirovich Konyagin turns 60”, Proc. Steklov Inst. Math., 303 (2018), 1–9  mathnet  crossref  crossref  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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