A characterization of reflexive Banach spaces
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- by Eva Matoušková and Charles Stegall PDF
- Proc. Amer. Math. Soc. 124 (1996), 1083-1090 Request permission
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
- Jonathan M. Borwein and Dominikus Noll, Second order differentiability of convex functions in Banach spaces, Trans. Amer. Math. Soc. 342 (1994), no. 1, 43–81. MR 1145959, DOI 10.1090/S0002-9947-1994-1145959-4
- J. P. R. Christensen, Topology and Borel structure, North-Holland Mathematics Studies, Vol. 10, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1974. Descriptive topology and set theory with applications to functional analysis and measure theory. MR 0348724
- Mahlon M. Day, Normed linear spaces, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 21, Springer-Verlag, New York-Heidelberg, 1973. MR 0344849
- Robert C. James, Weak compactness and reflexivity, Israel J. Math. 2 (1964), 101–119. MR 176310, DOI 10.1007/BF02759950
Additional Information
- Eva Matoušková
- 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
- 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
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1083-1090
- MSC (1991): Primary 46B10; Secondary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-96-03093-6
- MathSciNet review: 1301517