Chebyshev subspaces of L1 with linear metric projection

Abstract

In this note we consider Chebyshev subspaces (i.e., those that contain a unique nearest element to every point) of real L 1 = L 1[0, 1]. The result we prove is a characterization of those subspaces which are Chebyshev with linear metric projections (nearest point maps). We also give an example of a Chebyshev subspace whose metric projection is not linear.