BEST COAPPROXIMATION IN L1 ;X

Abstract

Let X be a real Banach space and let G be a closed subset of X. The set G is called coproximinal in X if for each x ∈ X, there exists y0 ∈ G such that ky − y0k ≤ kx − yk , for all y ∈ G. In this paper, we study coproximinality of L ∞ µ, G in L ∞ µ, X , when G is either separable or reflexive coproximinal subspace of X.