APPLICATION OF BISHOP-PHELPS THEOREM IN THE APPROXIMATION THEORY

In this paper we apply the Bishop-Phelps Theorem to show that if X is a Banach space and G⊆X is a maximal subspace so that G⊥={x∗∈X∗∣x∗(y)=0;∀y∈G} is an L-summand in X∗, then L1(Ω,G) is contained in a maximal proximinal subspace of L1(Ω,X).