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Matematicheskie Zametki, 1975, Volume 18, Issue 4, Pages 473–488 (Mi mzm9962)  

This article is cited in 6 scientific papers (total in 6 papers)

Metric projection onto finite-dimensional subspaces of C and L

V. I. Berdyshev

Institute of Mathematics and Mechanics of the General Science Center, Academy of Sciences of the USSR
Abstract: In the space C(Q) of real functions that are continuous on the compact set Q, a finite-dimensional subspace P will have a uniformly continuous metric projection if and only if Q is a finite sum of compact sets Qi, and either P is on each Qi a one-dimensional Chebyshev space, or \mathrm{x(t)\equiv0\mathrm} for any x belonging to P. The metric projection onto any finite-dimensional subspace of the space L[a,b] of real integrable functions is not uniformly continuous.
Received: 30.12.1974
English version:
Mathematical Notes, 1975, Volume 18, Issue 4, Pages 871–879
DOI: https://doi.org/10.1007/BF01153037
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: V. I. Berdyshev, “Metric projection onto finite-dimensional subspaces of C and L”, Mat. Zametki, 18:4 (1975), 473–488; Math. Notes, 18:4 (1975), 871–879
Citation in format AMSBIB
\Bibitem{Ber75}
\by V.~I.~Berdyshev
\paper Metric projection onto finite-dimensional subspaces of $\mathrm{C}$ and $\mathrm{L}$
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 4
\pages 473--488
\mathnet{http://mi.mathnet.ru/mzm9962}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=427926}
\zmath{https://zbmath.org/?q=an:0318.41025}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 4
\pages 871--879
\crossref{https://doi.org/10.1007/BF01153037}
Linking options:
  • https://www.mathnet.ru/eng/mzm9962
  • https://www.mathnet.ru/eng/mzm/v18/i4/p473
  • This publication is cited in the following 6 articles:
    1. A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. I. G. Tsarkov, “Ustoichivost otnositelnogo chebyshëvskogo proektora v poliedralnykh prostranstvakh”, Tr. IMM UrO RAN, 24, no. 4, 2018, 235–245  mathnet  crossref  elib
    3. K. V. Chesnokova, “The Linearity Coefficient of Metric Projections onto One-Dimensional Chebyshev Subspaces of the Space $C$”, Math. Notes, 96:4 (2014), 556–562  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. P. A. Borodin, “The Linearity Coefficient of the Metric Projection onto a Chebyshev Subspace”, Math. Notes, 85:1 (2009), 168–175  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. “Vitalii Ivanovich Berdyshev”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S1–S9  mathnet  crossref  isi
    6. P. V. Al'brecht, “Orders of moduli of continuity of operators of almost best approximation”, Russian Acad. Sci. Sb. Math., 83:1 (1995), 1–22  mathnet  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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