Geodesic
The Linearity Coefficient of the Metric Projection onto a Chebyshev Subspace
Matematičeskie zametki, Tome 85 (2009) no. 2, pp. 180-188.

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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. 
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P. A. Borodin. The Linearity Coefficient of the Metric Projection onto a Chebyshev Subspace. Matematičeskie zametki, Tome 85 (2009) no. 2, pp. 180-188. http://geodesic.mathdoc.fr/item/MZM_2009_85_2_a1/

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