On Simultaneous Farthest Points in L∞(I,X)‎

Abstract EN

Let X be a Banach space and let G be a closed bounded subset of X.

For (x1,x2,…,xm)∈Xm, we set ρ(x1,x2,…,xm,G)=sup{max1≤i≤m‖xi−y‖:y∈G}.

The set G is called simultaneously remotal if, for any (x1,x2,…,xm)∈Xm, there exists g∈G such that ρ(x1,x2,…,xm,G)=max1≤i≤m‖xi−g‖.

In this paper, we show that if G is separable simultaneously remotal in X, then the set of ∞-Bochner integrable functions, L∞(I,G), is simultaneously remotal in L∞(I,X).

Some other results are presented.