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Mat. Zametki, 2009, Volume 85, Issue 2, Pages 180–188 (Mi mz4507)  

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

The Linearity Coefficient of the Metric Projection onto a Chebyshev Subspace

P. A. Borodin

M. V. Lomonosov Moscow State University

Abstract: The linearity coefficient $\lambda(Y)$ of a metric projection $P_Y$ onto a subspace $Y$ in a Banach space $X$ is determined. This coefficient turns out to be related to the Lipschitz norm of the operator $P_Y$. It is proved that, for any Chebyshev subspace $Y$ in the space $C$ or $L_1$, either $\lambda(Y)=1$ (which corresponds to the linearity of $P_Y$) or $\lambda(Y)\le 1/2$.

Keywords: metric projection, linearity coefficient, Chebyshev subspace, Lipschitz norm

DOI: https://doi.org/10.4213/mzm4507

Full text: PDF file (473 kB)
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English version:
Mathematical Notes, 2009, 85:1, 168–175

Bibliographic databases:

UDC: 517.982.256
Received: 13.12.2008
Revised: 20.05.2008

Citation: P. A. Borodin, “The Linearity Coefficient of the Metric Projection onto a Chebyshev Subspace”, Mat. Zametki, 85:2 (2009), 180–188; Math. Notes, 85:1 (2009), 168–175

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. K. V. Chesnokova, “The mapping taking three points of a Banach space to their Steiner point”, Moscow University Mathematics Bulletin, 71:2 (2016), 71–74  mathnet  crossref  mathscinet  isi
    3. E. A. Antonenko, “A weakly supercritical mode in a branching random walk”, Moscow University Mathematics Bulletin, 71:2 (2016), 68–70  mathnet  crossref  mathscinet  isi
    4. P. A. Borodin, Yu. Yu. Druzhinin, K. V. Chesnokova, “Finite-Dimensional Subspaces of $L_p$ with Lipschitz Metric Projection”, Math. Notes, 102:4 (2017), 465–474  mathnet  crossref  crossref  mathscinet  isi  elib
    5. B. B. Bednov, P. A. Borodin, K. V. Chesnokova, “Existence of Lipschitz selections of the Steiner map”, Sb. Math., 209:2 (2018), 145–162  mathnet  crossref  crossref  adsnasa  isi  elib
    6. K. V. Chesnokova, “Steiner mapping of three points on Euclidean plane”, Moscow University Mathematics Bulletin, 73:1 (2018), 17–23  mathnet  crossref  mathscinet  zmath  isi
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