A Geometrical Characterization of the C(K) and C0(K) Spaces Original Research Article

In this paper we present, among other related results, the following geometrical characterization of C(K) and C0(K) spaces. Let X be a Banach space. Let r(A), rG(A), and E0(A) denote the Chebyshev radius of A, the Chebyshev radius of A relative to G, and the set of Chebyshev centers of A, respectively. We prove that X is isometric to a C(K) or C0(K) space if and only if rG(A)=r(A)+dist(E0(A), G) for every nonempty bounded subset A and nonempty subset G of X.