Skip to main content
Log in

Factoring operators through Banach lattices not containingC(0,1)

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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.

References

  1. Abramovic, J.A.: Weakly compact sets in topologicalK-spaces. Teor. Funkcii Funkcional. Anal. i Prilozen15, 27–35 (1972) (Russian)

    Google Scholar 

  2. Aliprantis, C.D., Burkinshaw, O.: Factoring compact and weakly compact operators through reflexive Banach lattices. Trans. Am. Math. Soc.283, 369–381 (1984)

    Google Scholar 

  3. Aliprantis, C.D., Burkinshaw, O.: Positive Operators. New York: Academic Press 1985

    Google Scholar 

  4. Davis, W.J., Figiel, T., Johnson, W.B., Pelczynski, A.: Factoring weakly compact operators. J. Funct. Anal.17, 311–327 (1974)

    Google Scholar 

  5. Diestel, J., Uhl, J.J. Jr.: Vector measures. Math. Surveys15, Am. Math. Soc. (1977)

  6. Figiel, T., Ghoussoub, N., Johnson, W.B.: On the structure of non-weakly compact operators on Banach lattices. Math. Ann.257, 317–334 (1981)

    Google Scholar 

  7. Figiel, T., Johnson, W.B., Tzafriri, L.: On Banach lattices and spaces having local unconditional structure with applications to Lorentz function spaces. J. Approximation Theory13, 395–412 (1975)

    Google Scholar 

  8. Ghoussoub, N., Positive embeddings ofC(Δ), L 1, l(Δ) and\((\sum\limits_n { \oplus l_\infty ^n } )_{l_1 } \). Math. Ann.262, 461–472 (1983)

    Google Scholar 

  9. Ghoussoub, N., Johnson, W.B.: Counterexamples to several problems on the factorization of bounded linear operators. Proc. Am. Math. Soc.92, 233–238 (1984)

    Google Scholar 

  10. Ghoussoub, N., Johnson, W.B.: On subspaces of Banach lattices not containingC(Δ), (unpublished)

  11. Johnson, W.B., Maurey, B., Schechtman, G., Tzafriri, L.: Symmetric structures in Banach spaces. Mem. Am. Math. Soc.19, No. 217 (1979)

    Google Scholar 

  12. Johnson, W.B., Rosenthal, H.P., Zippin, M.: On bases, finite dimensional decompositions, and weaker structures in Banach spaces. Isr. J. Math.9, 488–506 (1971)

    Google Scholar 

  13. Johnson, W.B., Tzafriri, L.: Some more Banach spaces which do not have local unconditional structure. Houston J. Math.3, 55–60 (1977)

    Google Scholar 

  14. Johnson, W.B., Zippin, M.: On subspaces of quotients of\((\sum\limits_n {G_n } )_{l_p } \) and\((\sum\limits_n {G_n } )_{c_0 } \). Isr. J. Math.13, 311–316 (1972)

    Google Scholar 

  15. Lindenstrauss, J., Pelczynski, A.: Absolutely summing operators in ℒ p spaces and their applications. Studia Math.29, 275–326 (1968)

    Google Scholar 

  16. Lewis, D.R., Stegall, C.: Banach spaces whose duals are isomorphic tol 1(Δ). J. Funct. Anal.12, 177–187 (1973)

    Google Scholar 

  17. Lotz, H.P., Rosenthal, H.P.: Embeddings ofC(Δ) andL 1[0,1] in Banach lattices. Isr. J. Math.31, 169–179 (1978)

    Google Scholar 

  18. Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces I: Sequences spaces. Erg. Math. Grenzgebiete 92. Berlin, Heidelberg, New York: Springer 1977

    Google Scholar 

  19. Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II: Function spaces. Erg. Math. Grenzgeb. 97. Berlin, Heidelberg, New York: Springer 1979

    Google Scholar 

  20. Meyer-Nieberg, P.: Zur schwachen Kompaktheit in Banach-Verbänden. Math. Z.134, 303–315 (1973)

    Google Scholar 

  21. Pelczynski, A., Rosenthal, H.P.: Localization techniques inL p spaces. Studia Math.52, 263–289 (1975)

    Google Scholar 

  22. Rosenthal, H.P.: On subspaces ofL p. Ann. Math.97, 344–373 (1973)

    Google Scholar 

  23. Rosenthal, H.P.: A characterization of Banach spaces containingl 1. Proc. Nat. Acad. Sci.71, 2411–2413 (1974)

    Google Scholar 

  24. Rosenthal, H.P.: A characterization ofc o and some remarks concerning the Grothendieck property. The Longhorn Notes, Univ. Texas Austin (1982–83), 95–108

  25. Schaefer, H.H.: Banach lattices and positive operators. Berlin, Heidelberg, New York: Springer 1974

    Google Scholar 

  26. Singer, I.: Bases in Banach spaces I. Berlin, Heidelberg, New York: Springer 1970

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported in part by NSERC A4808 (Canada)

Supported in part NSF DMS 8316627 and DMS 8500764

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ghoussoub, N., Johnson, W.B. Factoring operators through Banach lattices not containingC(0,1). Math Z 194, 153–171 (1987). https://doi.org/10.1007/BF01161965

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01161965

Navigation