Best approximation in polyhedral Banach spaces
The authors study conditions under which the metric projection of a polyhedral Banach space \(X\) onto a closed subspace \(Y\) is Hausdorff lower or upper semicontinuous. The paper is organized as follows. Section 0 is an introduction. Section 1 contains notation concerning Banach spaces, followed by definitions and preliminary facts on polyhedral Banach spaces. Section 2 is a collection of preliminaries concerning metric projections onto closed subspaces. Sections 3 and 4 deal with (semi)continuity properties of the metric projection \(P_Y\) under polyhedrality-type assumptions on \(X\). Section 5 contains results on the proximinality of subspaces and polyhedrality of quotients. Sections 6, 7 and 8 contain one example each. These examples illustrate the importance of some of the hypotheses in the main results.
scientific article; zbMATH DE number 5965565
scientific article