Weak* derived sets of convex sets in duals of non-reflexive spaces

摘要

We investigate weak* derived sets, that is the sets of weak* limits of bounded nets, of convex subsets of duals of non-reflexive Banach spaces and their possible iterations. We prove that a dual space of any non-reflexive Banach space contains convex subsets of any finite order and a convex subset of order omega + 1. (C) 2021 Elsevier Inc. All rights reserved.