A conjecture of Godefroy concerning James' theorem

Hermann Pfitzner (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

In this note we look at the interdependences between James' theorem and the boundary problem. To do so we show a variant of James' sup-theorem for C(K)-spaces conjectured by Godefroy: in order to know that a bounded weakly closed subset of a C(K)- space is weakly compact it is enough to test the sup-attainment only for measures with countable support.

Domaines: Analyse fonctionnelle [math.FA]

Hermann Pfitzner. A conjecture of Godefroy concerning James' theorem. Quaterly Journal of Mathematics (The), 2013, 64 (2), pp.547-553. ⟨hal-00663001⟩