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Israel Journal of Mathematics

, Volume 1, Issue 3, pp 139–148 | Cite as

On operators which attain their norm

  • Joram Lindenstrauss
Article

Abstract

The following problem is considered. LetX andY be Banach spaces. Are those operators fromX toY which attain their norm on the unit cell ofX, norm dense in the space of all operators fromX toY? It is proved that this is always the case ifX is reflexive. In general the answer is negative and it depends on some convexity and smoothness properties of the unit cells inX andY. As an application a refinement of the Krein-Milman theorem and Mazur’s theorem concerning the density of smooth points, in the case of weakly compact sets in a separable space, is obtained.

Keywords

Banach Space Extreme Point Convex Space Normed Linear Space Separable Banach Space 
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.

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Copyright information

© Hebrew University 1963

Authors and Affiliations

  • Joram Lindenstrauss
    • 1
    • 2
  1. 1.Yale UniversityNew Haven
  2. 2.University of WashingtonSeattle

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