Chebyshev centres and centrable sets

Abstract

In this paper we characterize real Banach spaces whose duals are isometric to L¹(μ) spaces (the so-called L¹-predual spaces) as those spaces in which every finite set is centrable. For a locally compact, non-compact set X and for an L¹-predual E, we give a complete description of the extreme points and denting points of the dual unit ball of , C_o(X,E), equipped with the diameter norm.