Skip to main content

Local unconditional structure in Banach spaces

  • Conference paper
  • First Online:
Banach Spaces of Analytic Functions

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 604))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. J. Bernau and H. E. Lacey, A local characterization of complex Banach lattices with order continuous norm, Studia Math., T. LVIII (1976), 1–28.

    MathSciNet  MATH  Google Scholar 

  2. D. Dacunha-Castelle and J. Krivine, Applications des ultraoroduits a l'etude des espaces et des algebres de Banach, Studia Math., T. XLI (1972), 315–334.

    MathSciNet  MATH  Google Scholar 

  3. E. Dubinsky, A. Pelczynski, and H. P. Rosenthal, On Banach spaces X for which Π2(ℒ∞,X)=B(ℒ∞,X), Studia Math., T. XLIV (1972), 617–648.

    MathSciNet  MATH  Google Scholar 

  4. T. Figiel, W. B. Johnson, and L. Tzafriri, On Banach lattices and spaces having local unconditional structure with applications to Lorentz sequence spaces, J. Approx. Theory, 13 (1975), 297–312.

    Article  MathSciNet  MATH  Google Scholar 

  5. Y. Gordon and D. R. Lewis, Absolutely summing operators and local unconditional structures, Acta. Math., 133 (1974), 27–48.

    Article  MathSciNet  MATH  Google Scholar 

  6. W. B. Johnson, On finite dimensional subspaces of Banach spaces with local unconditional structure, Studia Math., 51 (1974), 225–240.

    MathSciNet  MATH  Google Scholar 

  7. W. B. Johnson and L. Tzafriri, Some more Banach spaces which do not have local unconditional structure, preprint.

    Google Scholar 

  8. J. L. Krivine, Sur les espaces isomorphes a ℓp, Séminaire Maurey-Schwartz, 1974–75, No. 12.

    Google Scholar 

  9. H. Elton Lacey, The Isometric Theory of Classical Banach Spaces. Springer-Verlag, Grund. Band 208, New York, 1974.

    Book  MATH  Google Scholar 

  10. J. Lindenstrauss and A. Pelczynski, Absolutely summing operators in ℓp-spaces and their applications, Studia Math., T. XXIX (1968), 275–326.

    MathSciNet  MATH  Google Scholar 

  11. J. Lindenstrauss and H. P. Rosenthal, The ℒp spaces, Israel J. Math., 7 (1969), 325–349.

    Article  MathSciNet  MATH  Google Scholar 

  12. B. Maurey and G. Pisier, Caractérisation d'une classe d'espaces de Banach par des propriétés de series aléatoires vectorielles, C. R. Acad. Sci., Paris, t. 277 (1973), Serie A, 687–690.

    MathSciNet  MATH  Google Scholar 

  13. P. Meyer-Nieberg, Charakterisierung einiger topologischer und ordnungs-theoretischer Eigenshaften von Banach-verbänden mit Hilfe disjunkter Folgen., Arch. Math., 24 (1973), 640–647.

    Article  MathSciNet  MATH  Google Scholar 

  14. A. Pelczynski, Banach spaces of analytic functions and absolutely summing operators, Lectures notes of Kent Conference, August, 1976, p. 155.

    Google Scholar 

  15. A. Pelczynski, Projections in certain Banach spaces, Studia Math., 19 (1960), 209–228.

    MathSciNet  MATH  Google Scholar 

  16. A. Pietsch, Absolutely p-summing operators in ℒp-spaces, Bull. Soc. Math., France Mem., 31–32 (1972), 285–315.

    MathSciNet  MATH  Google Scholar 

  17. J. R. Retherford, Applications of Banach ideals of operators, Bull. Amer. Math. Soc., 81 (1975), 978–1012.

    Article  MathSciNet  MATH  Google Scholar 

  18. Schaefer, H. H., Banach Lattices and Positive Operators. Springer-Verlag, New York, Grund. Band. 215 (1974).

    Book  MATH  Google Scholar 

  19. J. Stern, Propriétés locales et ultrapuissances d'espaces de Banach. Séminaire Maurey-Schwartz (1974–75), No. 7.

    Google Scholar 

  20. L. Tzafriri, Reflexivity in Banach lattices and their subspaces, J. Functional Analysis, 10 (1972), 1–18.

    Article  MathSciNet  MATH  Google Scholar 

  21. __, Remarks on contractive projections in Lp spaces, Israel J. Math., 7 (1969), 9–15.

    Article  MathSciNet  MATH  Google Scholar 

  22. M. Zippin, On bases in Banach spaces. Thesis: Hebrew University, Jerusalem, Israel.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

J. Baker C. Cleaver J. Diestel

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Springer-Verlag

About this paper

Cite this paper

Lacey, H.E. (1977). Local unconditional structure in Banach spaces. In: Baker, J., Cleaver, C., Diestel, J. (eds) Banach Spaces of Analytic Functions. Lecture Notes in Mathematics, vol 604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069205

Download citation

  • DOI: https://doi.org/10.1007/BFb0069205

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08356-6

  • Online ISBN: 978-3-540-37262-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics