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Acta Mathematica

, Volume 126, Issue 1, pp 165–193 | Cite as

Banach spaces whose duals areL 1 spaces and their representing matrices

  • A. J. Lazar
  • J. Lindenstrauss
Article

Keywords

Banach Space Extreme Point Separable Banach Space Compact Hausdorff Space Choquet Simplex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1].
    Alfsen, E. M., On the geometry of Choquet simplexes.Math. Scand., 15 (1964), 97–110.MATHMathSciNetGoogle Scholar
  2. [2].
    Day, M. M.,Normed linear spaces. Springer, Berlin 1958.MATHGoogle Scholar
  3. [3].
    Edwards, D. A., Minimum stable wedges of semicontinuous functions.Math. Scand., 19 (1966), 15–26.MATHMathSciNetCrossRefGoogle Scholar
  4. [4].
    Effros, E. G., Structure in simplexes.Acta Math., 117 (1967), 103–121.MATHMathSciNetCrossRefGoogle Scholar
  5. [5].
    Goullet de Rugy, A.,Géométrie des simplexes. Centre de Documentation Universitaire et S.E.D.E.S., Paris 1969.MATHGoogle Scholar
  6. [6].
    Grothendieck, A., Une caractérisation vectorielle métrique des espaces L1.Canad. J. Math., 7 (1955), 552–561.MATHMathSciNetGoogle Scholar
  7. [7].
    Gurariî, V. I., Space of universal disposition, isotopic spaces and the Mazur problem on rotations of Banach spaces.Sibirskii Mat. Zh., 7 (1966), 1002–1013.MATHGoogle Scholar
  8. [8].
    Kakutani, S., Concrete representation of abstract M spaces.Ann. of Math., 42 (1941), 994–1024.MATHMathSciNetCrossRefGoogle Scholar
  9. [9].
    Kuratowski, K.,Topology, Vol. 1. Academic Press, New York, 1966.Google Scholar
  10. [10].
    Lazar, A. J., Spaces of affine continuous functions on simplexes.Trans. Amer. Math. Soc., 134 (1968), 503–525.MATHMathSciNetCrossRefGoogle Scholar
  11. [11].
    —, Polyhedral Banach spaces and extensions of compact operators.Israel J. Math., 7 (1969), 357–364.MATHMathSciNetGoogle Scholar
  12. [12].
    Lazar, A. J. &Lindenstrauss, J., On Banach spaces whose duals are L1 spaces.Israel J. Math., 4 (1966), 205–207.MATHMathSciNetGoogle Scholar
  13. [13].
    Léger, Ch., Une démonstration du théorème de A. J. Lazar.C. R. Acad. Sci. Paris, 265 (1967), 830–831.MATHGoogle Scholar
  14. [14].
    Lindenstrauss, J., Extension of compact operators.Memoirs Amer. Math. Soc., No. 48, 1964.Google Scholar
  15. [15].
    Lindenstrauss, J. &Phelps, R. R., Extreme point properties of convex bodies in reflexive Banach spaces.Israel J. Math., 6 (1968), 39–48.MATHMathSciNetGoogle Scholar
  16. [16].
    Lindenstrauss, J. &Pełczynski, A., Absolutely summing operators in Lp spaces and their applications.Studia. Math., 29 (1968), 275–326.MATHMathSciNetGoogle Scholar
  17. [17].
    Lindenstrauss, J. &Wulbert, D. E., On the classification of the Banach spaces whose duals areL 1 spaces,J. Funct. Anal., 4 (1969), 332–349.MATHMathSciNetCrossRefGoogle Scholar
  18. [18].
    Michael, E. A., Continuous selections I.Ann. of Math., 63 (1956), 361–382.MATHMathSciNetCrossRefGoogle Scholar
  19. [19].
    Michael, E. A. &Pełczynski, A., Separable Banach spaces which admitl n approximations.Israel J. Math., 4 (1966), 189–198.MATHMathSciNetGoogle Scholar
  20. [20].
    Phelps, R. R., Infinite-dimensional compact convex polytopes.Math. Scand., 24, (1969), 5–26.MATHMathSciNetGoogle Scholar
  21. [21].
    —,Lectures on Choquet's theorem. Van Nostrand, Princeton 1966.MATHGoogle Scholar
  22. [22].
    Poulsen, E. T., A simplex with dense extreme points.Ann. Inst. Fourier (Grenoble), 11 (1961), 83–87.MATHMathSciNetGoogle Scholar
  23. [23].
    Zippin, M., On some subspaces of Banach spaces whose duals are L1 spaces.Proc. Amer Math. Soc., 23 (1969), 378–385.MATHMathSciNetCrossRefGoogle Scholar
  24. [24].
    Lazar, A. J., The unit ball in conjugate L1 spaces. (To appear).Google Scholar

Copyright information

© Almqvist & Wiksells Boktryckeri AB 1971

Authors and Affiliations

  • A. J. Lazar
    • 1
    • 2
    • 3
    • 4
  • J. Lindenstrauss
    • 1
    • 2
    • 3
    • 4
  1. 1.University of WashingtonSeattle
  2. 2.Louisiana State UniversityBaton RougeUSA
  3. 3.Hebrew UniversityJerusalemIsrael
  4. 4.University of CaliforniaBerkeleyUSA

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