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Israel Journal of Mathematics

, Volume 2, Issue 4, pp 249–250 | Cite as

A proof of the Dvoretzky-Rogers theorem

  • Ivan Singer
Article
  • 128 Downloads

Abstract

We give a new proof of the famous Dvoretzky-Rogers theorem ([2], Theorem 1), according to which a Banach spaceE is finite-dimensional if every unconditionally convergent series inE is absolutely convergent.

Keywords

Banach Space Integral Operator Normed Linear Space Convergent Series 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.

References

  1. 1.
    S. Banach and S. Mazur,Zur Theorie der linearen Dimension, Studia Math.,4 (1933), 100–112.zbMATHGoogle Scholar
  2. 2.
    A. Dvoretzky and C. A. Rogers,Absolute and unconditional convergence in normed linear spaces, Proc. Nat. Acad. Sci.,36 (1950), 192–197.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    A. Grothendieck,Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc., no. 16., (1955).Google Scholar
  4. 4.
    A. Pełczyński,A proof of the theorem of Grothendieck on the characterization of nuclear spaces (Russian), Prace Mat.,7 (1962), 155–167.MathSciNetGoogle Scholar

Copyright information

© Hebrew University 1964

Authors and Affiliations

  • Ivan Singer
    • 1
  1. 1.Institut de MathematiqueAcademie de la R. P. RoumaineRoumania

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