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Every weakly compact set can be uniformly embedded into a reflexive Banach space.
- Source :
-
Acta Mathematica Sinica . Jul2009, Vol. 25 Issue 7, p1109-1112. 4p. - Publication Year :
- 2009
-
Abstract
- Based on an application of the Davis-Figiel-Johnson-PelzyĹ›ki procedure, this note shows that every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banach space. As its application, we present the recent renorming theorems for reflexive spaces of Odell-Schlumprecht and Hájek-Johanis can be extended and localized to weakly compact convex subsets of an arbitrary Banach space. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 25
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 47488211
- Full Text :
- https://doi.org/10.1007/s10114-009-7545-5