This article is cited in 2 papers

The Linearity Coefficient of Metric Projections onto One-Dimensional Chebyshev Subspaces of the Space $C$

K. V. Chesnokova

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 517.982.256

Received: 20.11.2012
Revised: 19.11.2013

DOI: 10.4213/mzm10228

 English version: Mathematical Notes, 2014, 96:4, 556–562

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