Error estimates and Lipschitz constants for best approximation in continuous function spaces (Q1904181)

Let \(G\) be a finite dimensional subspace of the Banach space \(C_0 (T)\) of all real-valued continuous functions on a locally compact Hausdorff space \(T\) which vanish at infinity. Using a structural characterization of the metric projection \(P_G (f)\), \(f\in C_0 (T)\) a sharp lower bound of the strong unicity constant [see \textit{W. Li}, J. Approximation Theory 56, 164-184 (1989; Zbl 0672.41020)]\ and exact Lipschitz constant for \(P_G\) are obtained. Construction of functions with desired properties are also given.