Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46B10, 46B20

Retrieve articles in all journals with MSC (1991): 46B10, 46B20

Additional Information

Eva Matousková
Affiliation: Department of Mathematical Analysis Charles University Sokolovská 83 CZ-18600 Prague, Czech Republic

Charles Stegall
Affiliation: Institut für Mathematik Johannes Kepler Universität Altenbergerstraße A-4040 Linz, Austria

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

American Mathematical Society