Boundaries and generation of convex sets

Vladimir P. Fonf, Joram Llndenstrauss

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


We introduce a notion which is intermediate between that of taking the w*-closed convex hull of a set and taking the norm closed convex hull of this set. This notion helps to streamline the proof (given in [FLP]) of the famous result of James in the separable case. More importantly, it leads to stronger results in the same direction. For example: 1. Assume X is separable and non-reflexive and its unit sphere is covered by a sequence of balls {C i}i=1 of radius a 1. Then for every sequence of positive numbers {εi}i=1 tending to 0 there is an f ∈ X*, such that ∥ f ∥ = 1 and f(x) ≤ 1 - εi, whenever x ∈ C i, i = 1,2,.. .. 2. Assume X is separable and non-reflexive and let T: Y → X* be a bounded linear non-surjective operator. Then there is an f ∈ X* which does not attain its norm on BX such that f ∉ T (Y).

Original languageEnglish
Pages (from-to)157-172
Number of pages16
JournalIsrael Journal of Mathematics
StatePublished - 1 Jan 2003

ASJC Scopus subject areas

  • General Mathematics


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