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A characterization of reflexive Banach spaces

Author(s): Eva Matousková; Charles Stegall
Journal: Proc. Amer. Math. Soc. 124 (1996), 1083-1090.
MSC (1991): Primary 46B10; Secondary 46B20
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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 $X=Z$ .

References:

1.: J.M. Borwein and D. Noll, Second order differentiability of convex functions in Banach spaces, Trans. Amer. Math. Soc. 342 (1994), 43--81. MR 94e:46076
2.: J.P.R. Christensen, Topology and Borel structure, North-Holland, Amsterdam, 1974. MR 50:1221
3.: M.M. Day, Normed linear spaces, Springer-Verlag, Berlin, 1973. MR 49:9588
4.: R.C. James, Weak compactness and reflexivity, Israel J. Math. 2 (1964), 101--119. MR 31:585

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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: 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 Osterreichische Akademische Austauschdienst
Communicated by: Dale Alspach
Copyright of article: Copyright 1996, American Mathematical Society


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