Debrecen, Hungaria: Institute of Mathematics, University of Debrecen
Abstract:
Let K be a weakly compact convex subset of a Banach space X. One version of the Markov-Kakutani Theorem states that if ℱ: (K, τw) → (K, τw) is a commutative family of continuous linear transformations, then ℱ has a common fixed point in K. Suppose now CC(X) is the collection of all non-empty compact convex subsets of X. We shall define a certain weak topology script J signw on CC(X) and get the above-mentioned version of the Markov-Kakutani Theorem extended to the hyperspace (CC(X), script J signw).
