Skip to Main content Skip to Navigation
Journal articles

Boundaries for Banach spaces determine weak compactness

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 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.
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00300244
Contributor : Hermann Pfitzner <>
Submitted on : Friday, July 18, 2008 - 9:50:09 AM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Tuesday, September 21, 2010 - 5:33:21 PM

Files

boundary-Hal.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Hermann Pfitzner. Boundaries for Banach spaces determine weak compactness. Inventiones Mathematicae, Springer Verlag, 2010, 182 (3), pp.585-607. ⟨10.1007/s00222-010-0267-6⟩. ⟨hal-00300244v2⟩

Share

Metrics

Record views

212

Files downloads

242