NEW RESULTS ON REMOTALITY IN BANACH SPACES

Abstract

A set E in a Banach space X is called remotal if for each x ∈ X, there exists an e ∈ E such that ∥x− e∥ = sup{∥x−e∥ : e ∈ E}.  If e is unique, E is called uniquely remotal.  One of the main results of this paper is: a weakly closed bounded set E in a reflexive Banach space is uniquely remotal if and only if the weak closed convex hull of E is uniquely remotal.