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On the structure of non-weakly compact operators on Banach lattices

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References

  1. Bourgain, J., Delbaen, F.: A special class of ℒ spaces. Acta Math. (to appear)

  2. Dacunha-Castelle, D., Schreiber, M.: Techniques probabilistes pour l'étude des problemes d'isomorphismes entre espaces de Banach. Ann. Inst. Poincaré10, 229–277 (1974)

    Google Scholar 

  3. Diestel, J.: Geometry of Banach spaces-selected topics. Lecture Notes. In Mathematics, Vol. 485. Berlin, Heidelberg, New York: Springer 1975

    Google Scholar 

  4. Enflo, P., Starbird, T.W.: Subspaces ofL 1 containingL 1. Studia Math.65, 203–225 (1979)

    Google Scholar 

  5. 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 

  6. Ghoussoub, N., Saab, E.: On the weak Radon-Nikodym property. Proc. A.M.S.81, 81–84 (1981)

    Google Scholar 

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

    Google Scholar 

  8. Hagler, J.: Some more Banach spaces which containl 1. Studia Math.46, 35–42 (1973)

    Google Scholar 

  9. Hagler, J., Johnson, W.B.: On Banach spaces whose dual balls are not weak*-sequentially compact. Israel J. Math.38, 325–330 (1977)

    Google Scholar 

  10. Hagler, J., Odell, E.W.: A Banach space not containingl 1 whose dual ball is not weak star sequentially compact. Illinois J. Math.22, 290–295 (1978)

    Google Scholar 

  11. Hagler, J., Stegall, C.: Banach spaces whose duals contain subspaces isomorphic toC[0, 1]*. J. Functional Analysis13, 233–251 (1973)

    Google Scholar 

  12. Haydon, R.: On Banach spaces which containl 1(Γ) and types of measures on compact spaces. Israel J. Math.28, 313–324 (1977)

    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., Maurey, B., Schechtman, G., Tzafriri, L.: Symmetric structures in Banach spaces. Memoir A.M.S.217 (1979)

  15. Juhasz, J.: Cardinal functions in topology. Math. Tract34 (1971)

  16. Kalton, N.: EmbeddingL 1 in a Banach lattice. Israel J. Math.31, 169–179 (1978)

    Google Scholar 

  17. Lindenstrauss, J., Pelczynski, L.: Contributions to the theory of classical Banach spaces. J. Funct. Analysis8, 225–249 (1971)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  22. Pelczynski, A.: Banach spaces on which every unconditionally converging operator is weakly compact. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.10, 641–648 (1962)

    Google Scholar 

  23. Pelczynski, A.: On Banach spaces containingL 1(μ). Studia Math.30, 231–246 (1968)

    Google Scholar 

  24. Rosenthal, H.P.: On injective Banach spaces and the spacesL (μ) for finite measures μ. Acta Math.124, 205–248 (1970)

    Google Scholar 

  25. Rosenthal, H.P.: On factors ofC[0, 1] with non-separable dual. Israel J. Math.13, 361–378 (1975)

    Google Scholar 

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

    Google Scholar 

  27. Schaeffer, H.H.: Banach lattices and positive operators. Berlin, Heidelberg, New York: Springer 1974

    Google Scholar 

  28. Tzafriri, L.: Reflexivity in Banach lattices and their subspaces. J. Functional Analysis10, 1–18 (1972)

    Google Scholar 

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Supported in part by NSF-MCS-80-02393

Supported in part by NSF-MCS-7903042

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Figiel, T., Ghoussoub, N. & Johnson, W.B. On the structure of non-weakly compact operators on Banach lattices. Math. Ann. 257, 317–334 (1981). https://doi.org/10.1007/BF01456502

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