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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2009 Volume 85, Issue 2, Pages 180–188 (Mi mzm4507)

This article is cited in 7 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.

UDC: 517.982.256

Received: 13.12.2008
Revised: 20.05.2008

DOI: 10.4213/mzm4507


 English version:
Mathematical Notes, 2009, 85:1, 168–175

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