Double-dual types over the Banach space C(K)

Let K be a compact Hausdorff space and C(K) the Banach space of all real-valued continuous functions on K , with the sup-norm. Types over C(K) (in the sense of Krivine and Maurey) can be uniquely represented by pairs ( ,u) of bounded real-valued functions on K , where is lower semicontinuous, u is upper semicontinuous, ≤ u, and (x) = u(x) for all isolated points x of K . A condition that characterizes the pairs ( ,u) that represent double-dual types over C(K) is given.