Proximinality of certain subspaces of \(C_ b(S;E)\)
Let S be a completely regular Hausdorff space and let E be a Banach space. Let \(C_ b(S;E)\) be the Banach space of all continuous and bounded functions from S into E, equipped with the supremum-norm \(\| f\| =\sup \{\| f(x)\|;\quad x\in S\}.\) Given a proximinal linear subspace V of E, we study conditions under which the space \(\{f\in C_ b(S;E)\); f(S)\(\subset V\}\) is also proximinal in \(C_ b(S;E)\).
scientific article; zbMATH DE number 4146785