Israel Journal of Mathematics

, Volume 17, Issue 2, pp 219–230 | Cite as

Some remarks on weakly compactly generated banach spaces

  • W. B. Johnson
  • J. Lindenstrauss


A simple example is given of a non WCG space whose dual is a WCG space with an unconditional basis. It is proved that ifX* is WCG andX is a subspace of a WCG space thenX itself is WCG.


Banach Space Smooth Banach Space Unconditional Basis Compact Hausdorff Space Density Character 
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  1. 1.
    D. Amir and J. Lindenstrauss,The structure of weakly compact sets in Banach spaces, Ann. of Math.88 (1968), 35–46.CrossRefMathSciNetGoogle Scholar
  2. 2.
    W. J. Davis, T. Figiel, W. B. Johnson and A. Pelczynski,Factoring weakly compact operators, to appear.Google Scholar
  3. 3.
    R. C. James,A conjecture about l 1 subspaces, to appear.Google Scholar
  4. 4.
    K. John and V. Zizler,A renorming of dual spaces, Israel J. Math.12 (1972), 331–336.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    K. John and V. Zizler,Projections in dual weakly compactly generated Banach spaces, to appear in Studia Math.Google Scholar
  6. 6.
    K. John and V. Zizler,Smoothness and its equivalents in weakly compactly generated Banach spaces, to appear in J. Functional Analysis.Google Scholar
  7. 7.
    W. B. Johnson and E. Odell,Subspaces of L p which embed into l p,Compositio Math., to appear.Google Scholar
  8. 8.
    J. Lindenstrauss,Weakly compact sets — their topological properties and the Banach spaces they generate, Annals of Math. Studies69 (1972), 235–273.MathSciNetGoogle Scholar
  9. 9.
    J. Lindenstrauss and C. Stegall,On some examples of separable spaces whose duals are nonseparable but do not contain l 1, to appear.Google Scholar
  10. 10.
    G. W. Mackey,Note on a theorem of Murray, Bull, Amer. Math. Soc.52 (1946), 322–325.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    H. P. Rosenthal,The heredity problem for weakly compactly generated Banach spaces, Compositio Math., to appear.Google Scholar
  12. 12.
    A. Sobczyk,Projections of the space m on its subspace c 0, Bull. Amer. Math. Soc.47 (1941), 938–947.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    S. Troyanski,On locally uniformly convex and differentiable norms in certain nonseparable Banach spaces, Studia Math.37 (1971), 173–180.zbMATHMathSciNetGoogle Scholar
  14. 14.
    S. Troyanski,Equivalent norms and minimal systems in Banach spaces, Studia Math.43 (1972), 125–138.MathSciNetGoogle Scholar

Copyright information

© The Weizmann Science Press 1974

Authors and Affiliations

  • W. B. Johnson
    • 1
    • 2
  • J. Lindenstrauss
    • 1
    • 2
  1. 1.The Ohio State UniversityColumbusU. S. A.
  2. 2.The Hebrew University of JerusalemJerusalemIsrael

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