WEAK AND WEAK* TOPOLOGIES AND BRODSKII-MILMAN’S THEOREM ON HYPERSPACES
Thakyin Hu, Jui‐Chi Huang · Taiwanese Journal of Mathematics · 2009
Let K be a weakly compact, convex subset of a Banach space X with normal structure. Brodskii and Milman proved that there exists a point p ∈ K which is fixed under all isometries of K onto K. Suppose now WCC(X) is the collection of all non-empty weakly compact convex subsets of X. We shall define a certain weak topology Tw on WCC(X) and have the above-mentioned result extended to the hyperspace (WCC(X), Tw)