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

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.