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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A characterization
of reflexive Banach spaces


Authors: Eva Matousková and Charles Stegall
Journal: Proc. Amer. Math. Soc. 124 (1996), 1083-1090
MSC (1991): Primary 46B10; Secondary 46B20
MathSciNet review: 1301517
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Abstract: A Banach space $Z$ is not reflexive if and only if there exist a closed separable subspace $X$ of $Z$ and a convex closed subset $Q$ of $X$ with empty interior which contains translates of all compact sets in $X$. If, moreover, $Z$ is separable, then it is possible to put $X=Z$.


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Additional Information

Eva Matousková
Affiliation: Department of Mathematical Analysis \ Charles University \ Sokolovská 83 \ CZ-18600 Prague, Czech Republic
Email: eva@csmat.karlin.mff.cuni.cz

Charles Stegall
Affiliation: Institut für Mathematik \ Johannes Kepler Universität \ Altenbergerstraße \ A-4040 Linz, Austria
Email: stegall@caddo.bayou.uni-linz.ac.at

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03093-6
PII: S 0002-9939(96)03093-6
Keywords: Banach spaces, reflexivity, convexity
Received by editor(s): May 24, 1994
Received by editor(s) in revised form: August 18, 1994
Additional Notes: The first author was partially supported by a grant of the Ősterreichische Akademische Austauschdienst
Communicated by: Dale Alspach
Article copyright: © Copyright 1996 American Mathematical Society