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The Radon-Nikodym property and spaces of operators

  • Radon-nikodym Theorems for Vector Valued Measures
  • Conference paper
  • First Online:
Measure Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 541))

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Bibliography

  1. D. Amir and J. Lindenstrauss, The structure of weakly compact sets in Banach spaces. Ann. of Math., 88(1968), 35–46.

    Article  MathSciNet  MATH  Google Scholar 

  2. R. G. Bartle, N. Dunford, and J. T. Schwartz, Weak Compactness and vector measures, Canad. J. Math., 7(1955), 289–305.

    Article  MathSciNet  MATH  Google Scholar 

  3. S. Bochner, Additive set functions on groups, Ann. Math. (2) 40(1939), 769–799.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Diestel, The Radon-Nikodým property and the coincidence of integral and nuclear operators, Revue Roum. Math. 17(1972), 1611–1620.

    MathSciNet  MATH  Google Scholar 

  5. -, Applications of weak compactness and bases to vector measures and vectorial integration, Revue Roumaine Math., 18(1973), 211–224.

    MathSciNet  MATH  Google Scholar 

  6. J. Diestel and B. Faires, On vector measures, Trans. AMS, 198(1974), 253–271.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Diestel and B. Faires, Remarks on the classical Banach operator ideals, Proc. AMS, to appear.

    Google Scholar 

  8. J. Diestel and J. J. Uhl, Jr. The Radon-Nikodým theorem for Banach space valued measures, Rocky Mtn. Jour., to appear.

    Google Scholar 

  9. J. Diestel and J. J. Uhl, Jr., Topics in the Theory of Vector Measures, Notes presently being collected at Kent State University and the University of Illinois.

    Google Scholar 

  10. J. Dixmier, Les fonctionnnelles lineaires sur l’ensemble des operateurs bornés d’un espace de Hilbert, Ann. of Math., (2) 51(1950), 387–408.

    Article  MathSciNet  MATH  Google Scholar 

  11. P. Enflo, A counterexample to the approximation problem, Acta Math.

    Google Scholar 

  12. B. Faires, Grothendieck spaces and vector measures, Ph.D. dissertation, Kent State University, August, 1974.

    Google Scholar 

  13. B. Faires and T. J. Morrison, (as yet unpublished).

    Google Scholar 

  14. T. Figiel and W. B. Johnson, The approximation property does not imply the bounded approximation property, Proc. AMS, 41(1973), 197–200.

    Article  MathSciNet  MATH  Google Scholar 

  15. A. Grothendieck, Sur les applications linearies faiblement compactes d’espaces du type C(K), Canad. J. Math., 5(1953), 129–173.

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Memoirs of Amer. Math. Soc., 16(k955).

    Google Scholar 

  17. -, Resumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Matem. Sao Paolo, 8(1956), 1–79.

    MATH  Google Scholar 

  18. J. R. Holub, Reflexivity of L(E, F), Proc. AMS, 39(1973), 175–177.

    MathSciNet  MATH  Google Scholar 

  19. D. R. Lewis, Weak integrability in L1 spaces, preprint.

    Google Scholar 

  20. D. R. Lewis and C. Stegall, Banach spaces whose duals are isomorphic to ℓ1 (Γ), Jour. of Funcl. Anal., 12(1973), 177–187.

    Article  MathSciNet  MATH  Google Scholar 

  21. J. Lindenstrauss and C. Stegall, Examples of separable spaces which do not contain â„“1 and whose duals are nonseparable, to appear.

    Google Scholar 

  22. M. Metivier, Martingales à valeurs vectorielles. Applications à la dérivations des mesures vectorielles, Ann. Inst. Fourier (Grenoble) 17(1967), 175–208.

    Article  MathSciNet  MATH  Google Scholar 

  23. S. Moedomo and J. J. Uhl, Jr., Radon-Nikodým theorems for the Bochner and Pettis integrals, Pacific Journal Math., 38(1971), 531–536.

    Article  MathSciNet  MATH  Google Scholar 

  24. R. Schatten, Norm Ideals of Completely Continuous Operators. Springer-Verlag, Berlin, 1960.

    Book  MATH  Google Scholar 

  25. R. R. Phelps, Dentability and extreme points in Banach spaces, J. of Functional Analysis, 16(1974), 78–90.

    Article  MathSciNet  MATH  Google Scholar 

  26. A. Pietsch, Abbildungen von abstrakten Massen, Wiss. Zeit. Friedrich-Schiller Univ., 5(1965), 281–286.

    MathSciNet  MATH  Google Scholar 

  27. A. Persson and A. Pietsch, p-nukleare und p-integrale Abbildungen in Banachräumen, Studia Math., 33(1969), 19–62.

    MathSciNet  MATH  Google Scholar 

  28. A. Pietsch, Theorie der Operatorenideale, Friedrich-Schiller-Universitat, Jena, 1972.

    MATH  Google Scholar 

  29. M. A. Rieffel, The Radon-Nikodým theorem for the Bochner integral, Transactions of Amer. Math. Soc., 131(1968), 466–487.

    Article  MathSciNet  MATH  Google Scholar 

  30. E. Saab, Families absolument sommables et propriete de Radon-Nikodým, preprint.

    Google Scholar 

  31. H. H. Schaefer, Topological Vector Spaces. MacMillan and Sons, New York, 1966.

    MATH  Google Scholar 

  32. C. Stegall, The Radon-Nikodým property in conjugate Banach spaces, Trans. AMS.

    Google Scholar 

  33. A. E. Tong, Nuclear mappings on C(K), Math. Ann., 194(1971), 213–224.

    Article  MathSciNet  MATH  Google Scholar 

  34. J. J. Uhl, Jr., Orlicz spaces of finitely additive set functions, Studia Math., 29(1967), 19–58.

    MathSciNet  MATH  Google Scholar 

  35. J. J. Uhl, Jr. A note on the Radon-Nikodým property for Banach spaces, Revue Roum. Math., 17(1972), 113–115.

    MathSciNet  MATH  Google Scholar 

  36. A. Wilansky, Topics in Functional Analysis. Lecture Notes No. 45, Springer-Verlag, New York.

    Google Scholar 

  37. J. Diestel and T. J. Morrison, The Radon-Nikodým Property for the Space of Operators, submitted.

    Google Scholar 

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Authors and Affiliations

  1. Kent State University, Kent, Ohio

    J. Diestel

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  1. J. Diestel
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Alexandra Bellow Dietrich Kölzow

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© 1976 Springer-Verlag

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Diestel, J. (1976). The Radon-Nikodym property and spaces of operators. In: Bellow, A., Kölzow, D. (eds) Measure Theory. Lecture Notes in Mathematics, vol 541. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081054

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  • DOI: https://doi.org/10.1007/BFb0081054

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07861-6

  • Online ISBN: 978-3-540-38107-5

  • eBook Packages: Springer Book Archive

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