English

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

Functional Analysis 2021-11-29 v1

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 ω+1\omega + 1.

Keywords

Cite

@article{arxiv.2101.10684,
  title  = {Weak$^*$ derived sets of convex sets in duals of non-reflexive spaces},
  author = {Zdeněk Silber},
  journal= {arXiv preprint arXiv:2101.10684},
  year   = {2021}
}