Linear selections for the metric projection

AbstractA characterization is given of those proximinal subspaces of a normed linear space whose (set-valued) metric projections admit linear selections. This characterization is applied in each of the classical Banach spaces C0(T) and Lp (1 ⩽ p ⩽ ∞), resulting in an intrinsic characterization of those one-dimensional subspaces whose metric projections admit linear selections