Weak${}^{\ast }$ derived sets of convex sets in duals of non-reflexive spaces

Abstract

We investigate weak${}^{\ast }$ derived sets, that is the sets of weak${}^{\ast }$ 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 $\omega +1$.