A conjecture of Godefroy concerning James' theorem

Details A conjecture of Godefroy concerning James' theorem A conjecture of Godefroy concerning James' theorem

2012-01-26

arxiv.org/abs/1201.5471v1

Mathematics

Functional Analysis

to appear in Quarterly Journal of Math

Scientific paper

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.

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