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Israel Journal of Mathematics

, Volume 81, Issue 3, pp 297–299 | Cite as

The Dunford-Pettis property is not a three-space property

  • Jesús M. F. Castillo
  • Manuel González
Article

Abstract

An example of a Banach spaceX is shown which does not have the Dunford-Pettis property, while some subspaceY and the corresponding quotientX/Y have the hereditary Dunford-Pettis property.

Keywords

Banach Space Compact Operator Closed Subspace Canonical Basis Space Problem 
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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References

  1. [1]
    P. G. Casazza and T. J. Shura,Tsirelson’s Space, Lecture Notes in Mathematics 1363, Springer, Berlin, 1989.MATHGoogle Scholar
  2. [2]
    J. Diestel,A survey of results related to the Dunford-Pettis property, AMS Contemporary Math.2 (1980), 15–60.MathSciNetGoogle Scholar
  3. [3]
    H. Jarchow,The three space problem and ideals of operators, Math. Nachr.119 (1984), 121–128.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    M. I. Ostrovskii,Three spaces problem for the weak Banach-Saks property, Math. Notes38 (1985), 905–908.MathSciNetGoogle Scholar

Copyright information

© The Magnes Press 1993

Authors and Affiliations

  • Jesús M. F. Castillo
    • 1
  • Manuel González
    • 2
  1. 1.Departamento de MatemáticasUniversidad de ExtremaduraBadajozEspaña
  2. 2.Departamento de MatemáticasUniversidad de CantabriaSantanderEspaña

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