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The geometry of weak Radon-Nikodým sets in dual Banach spaces


Author: Lawrence H. Riddle
Journal: Proc. Amer. Math. Soc. 86 (1982), 433-438
MSC: Primary 46B20
DOI: https://doi.org/10.1090/S0002-9939-1982-0671210-2
MathSciNet review: 671210
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Abstract: Geometric characterizations in terms of trees, extreme points and dentability are presented for weak*-compact absolutely convex sets that have the Radon-Nikodym property for the Pettis integral.


References [Enhancements On Off] (What's this?)

  • [1] M. Day, Normed linear spaces, 3rd ed., Ergebnisse der Math. und ihrer Grenzgebiete, Springer-Verlag, Berlin and New York, 1973. MR 0344849 (49:9588)
  • [2] J. Diestel and J. J. Uhl, Jr., Vector measures, Math. Surveys, no. 15, Amer. Math. Soc., Providence, R. I., 1977. MR 0453964 (56:12216)
  • [3] N. Ghoussoub and E. Saab, On the weak Radon-Nikodym property, Proc. Amer. Math. Soc. 81 (1981), 81-84. MR 589141 (81j:46068)
  • [4] R. Haydon, Some more characterizations of Banach spaces containing $ {l_1}$, Math. Proc. Cambridge Philos. Soc. 80 (1976), 269-276. MR 0423047 (54:11031)
  • [5] L. Janicka, Some measure-theoretical characterization of Banach spaces, not containing $ {l_1}$, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), 561-565. MR 581552 (81i:28012)
  • [6] P. W. McCartney, Neighborly bushes and the Radon-Nikodym property for Banach spaces, Pacific J. Math. 87 (1980), 157-168. MR 590873 (82g:46045)
  • [7] I. Namioka and R. R. Phelps, Banach spaces which are Asplund spaces, Duke Math. J. 42 (1975), 735-750. MR 0390721 (52:11544)
  • [8] L. H. Riddle, E. Saab and J. J. Uhl, Jr., Sets with the weak Radon-Nikodym property in dual Banach spaces, Indiana Univ. Math. J. (to appear). MR 703283 (84h:46028)
  • [9] L. H. Riddle and J. J. Uhl, Jr., The fine line between Asplund spaces and spaces not containing a copy of $ {l_1}$, preprint.
  • [10] H. P. Rosenthal, A characterization of Banach spaces containing $ {l_1}$, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411-2413. MR 0358307 (50:10773)
  • [11] E. Saab and P. Saab, On Banach spaces not containing $ {l_1}$, Pacific J. Math, (to appear).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0671210-2
Article copyright: © Copyright 1982 American Mathematical Society

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