Skip to main content Accessibility help
  • Print publication year: 2020
  • Online publication date: March 2020

Appendix A - Zorn’s Lemma



We define weak convergence and give some examples, including a proof of Schur’s Theorem that weak and strong convergence coincide in l^1. We also show that closed convex subsets of Banach spaces are weakly closed. We then introduce weak-* convergence and prove two powerful weak compactness theorems: Helly’s Theorem for weak-* convergence in the duals of separable Banach spaces and a weak sequential compactness theorem in reflexive Banach spaces.