Skip to main content
Log in

On Banach spaces whose dual balls are not weak sequentially compact

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

Theorem 1. LetX be a Banach space. (a) IfX has a closed subspace in which no normalized sequence converges weak to zero, thenl 1 is isomorphic to a subspace ofX. (b) IfX contains a bounded sequence which has no weak convergent subsequence, thenX contains a separable subspace whose dual is not separable.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Hagler,A counterexample to several questions about Banach spaces, Studia Math., to appear.

  2. R. Haydon,On Banach spaces which contain l 1 (τ) and types of measures on compact spaces, preprint.

  3. W. B. Johnson and H. P. Rosenthal,On w -basic sequences and their application to the study of Banach spaces, Studia Math.43 (1972), 77–92.

    MathSciNet  Google Scholar 

  4. B. Josefson,Weak sequential convergence in the dual of a Banach space does not imply norm convergence, Ark. Mat.13 (1975), 79–89.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Lindenstrauss and L. Tzafriri,Classical Banach spaces, Springer lecture notes 338.

  6. A. Nissenzweig,w sequential convergence, Israel J. Math.22 (1975), 266–272.

    MathSciNet  Google Scholar 

  7. A. Peŀczyński,On Banach spaces containing L 1 (μ), Studia Math.30 (1968), 231–246.

    MathSciNet  Google Scholar 

  8. H. P. Rosenthal,A characterization of Banach spaces containing l1, Proc. Nat. Acad. Sci. U.S.A.71 (1974), 2411–2413.

    Article  MATH  MathSciNet  Google Scholar 

  9. C. Stegall,The Radon-Nikodym property in conjugate Banach spaces, Trans. Amer. Math. Soc.206 (1975), 213–223.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The second-named author was supported in part by NSF-MPS 72-04634-A03.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hagler, J., Johnson, W.B. On Banach spaces whose dual balls are not weak sequentially compact. Israel J. Math. 28, 325–330 (1977). https://doi.org/10.1007/BF02760638

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02760638

Keywords

Navigation