Double-dual types over the Banach spaceC(K)

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