(untitled) (Analysis in Theory and Applications, 2011)
In this paper we apply Bishop-Phelps property to show that if X is a Banach space and G X is the maximal subspace so that G^= {x^* X^*|x^*(y) = 0; y G} is an L-summand in X^*, then L^1(Ω,G) is contained in a maximal proximinal subspace of L^1(Ω,X).