Abstract
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; Ay ∈ G} is an L-summand in X*, then L1(Ω,G) is contained in a maximal proximinal subspace of L1(Ω,X).
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