Boundaries for Banach spaces determine weak compactness

Details Boundaries for Banach spaces determine weak compactness Boundaries for Banach spaces determine weak compactness

2008-07-17

arxiv.org/abs/0807.2810v2

Mathematics

Functional Analysis

Scientific paper

A boundary for a Banach space is a subset of the dual unit sphere with the property that each element of the Banach space attains its norm on an element of that subset. Trivially, the pointwise convergence with respect to such a boundary is coarser than the weak topology on the Banach space. Godefroy's Boundary Problem asks whether nevertheless both topologies have the same bounded compact sets. This paper contains the answer in the positive.

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