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

Abstract

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.

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Keywords

• Weak* derived set
• Weak* sequential closure
• Convex set
• Non-reflexive Banach space