Weak-topology and Alaoglu's theorem on hyperspace

Let X be a Banach space and X* its dual space. The classical Alaoglu theorem states that closed balls B-r* of X* are weak*-compact. Suppose now W*CC(X*) is the collection of all non-empty weak*-compact, convex subsets of X*. We shall define a certain weak*-topology T-w* on the hyperspace W*CC(X*). If X is separable, we shall prove that closed balls B-r* of W*CC(X*) are weak*-compact (T-w*-compact)