Banach Spaces with Weak Sequentially Compact Dual Balls

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


Alaoglu’s theorem ensures that every bounded sequence (x n * ) in X* has a weak* convergent subnet. When can one actually extract a weak* convergent subsequence? As yet, no one knows. In this chapter a few of the most attractive conditions assuring the existence of such subsequences are discussed.


Banach Space Linear Span Convergent Subsequence Separable Banach Space Compact Hausdorff Space 
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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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