Israel Journal of Mathematics

, Volume 9, Issue 4, pp 511–512 | Cite as

A counterexample for a sup theorem in normed spaces

  • Robert C. James


An example is given of a normed linear space that is not complete but for which each continuous linear functional attains its supremum on the unit ball.


Banach Space Extreme Point Unit Ball NORMED Space Convex Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    M. M. Day,Normed Linear Spaces, Academic Press, 1962.Google Scholar
  2. 2.
    R. C. James,Characterizations of reflexivity, Studia Math.23 (1964), 205–216.zbMATHMathSciNetGoogle Scholar

Copyright information

© The Weizmann Science Press of Israel 1971

Authors and Affiliations

  • Robert C. James
    • 1
  1. 1.Claremont Graduate SchoolClaremont

Personalised recommendations