The Josefson-Nissenzweig Theorem

  • Joseph Diestel
Part of the Graduate Texts in Mathematics book series (GTM, volume 92)


From Alaoglu’s theorem and the F. Riesz theorem, we can conclude that for infinite-dimensional Banach spaces X the weak* topology and the norm topology in X* differ. Can they have the same convergent sequences? The answer is a resounding “no!” and it is the object of the present discussion. More precisely we will prove the following theorem independently discovered by B. Josef son and A. Nissenzweig.


Banach Space Real Banach Space Null Sequence Unit Vector Basis Szlenk Index 
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Copyright information

© Springer-Verlag New York, Inc. 1984

Authors and Affiliations

  • Joseph Diestel
    • 1
  1. 1.Department of Math SciencesKent State UniversityKentUSA

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