This is an announcement for the paper "Boundaries for Banach spaces determine weak compactness" by Hermann Pfitzner.

Abstract: 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 boundary. 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.

Archive classification: math.FA

Mathematics Subject Classification: 46B20

The source file(s), boundary.tex: 30948 bytes, is(are) stored in gzipped form as 0807.2810.gz with size 10kb. The corresponding postcript file has gzipped size 76kb.

Submitted from: Hermann.Pfitzner@univ-orleans.fr

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