Geodesic
The Linearity Coefficient of Metric Projections onto One-Dimensional Chebyshev Subspaces of the Space~$C$
Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 588-595

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with the operator of metric projection onto an arbitrary one-dimensional Chebyshev subspace $\langle\varphi\rangle$ of the space $C[K]$ of real-valued functions defined and continuous on a Hausdorff compact set $K$. The linearity coefficient of the operator is calculated in terms of the parameters of the generating function $\varphi$. As a consequence, a new estimate of the Lipschitz constant of the operator is obtained.
Keywords: metric projection operator, Chebyshev subspace, Hausdorff compact set $K$, Lipschitz constant of an operator, Lipschitz condition, Banach space. 
@article{MZM_2014_96_4_a9,
     author = {K. V. Chesnokova},
     title = {The {Linearity} {Coefficient} of {Metric} {Projections} onto {One-Dimensional} {Chebyshev} {Subspaces} of the {Space~}$C$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {588--595},
     publisher = {mathdoc},
     volume = {96},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a9/}
}
TY  - JOUR
AU  - K. V. Chesnokova
TI  - The Linearity Coefficient of Metric Projections onto One-Dimensional Chebyshev Subspaces of the Space~$C$
JO  - Matematičeskie zametki
PY  - 2014
SP  - 588
EP  - 595
VL  - 96
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a9/
LA  - ru
ID  - MZM_2014_96_4_a9
ER  - 
%0 Journal Article
%A K. V. Chesnokova
%T The Linearity Coefficient of Metric Projections onto One-Dimensional Chebyshev Subspaces of the Space~$C$
%J Matematičeskie zametki
%D 2014
%P 588-595
%V 96
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a9/
%G ru
%F MZM_2014_96_4_a9
K. V. Chesnokova. The Linearity Coefficient of Metric Projections onto One-Dimensional Chebyshev Subspaces of the Space~$C$. Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 588-595. http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a9/