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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- [1] Mahlon M. Day, Normed linear spaces, 3rd ed., Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 21. MR 0344849
- [2] J. Diestel and J. J. Uhl Jr., Vector measures, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis; Mathematical Surveys, No. 15. MR 0453964
- [3] Nassif Ghoussoub and Elias Saab, On the weak Radon-Nikodým property, Proc. Amer. Math. Soc. 81 (1981), no. 1, 81–84. MR 589141, https://doi.org/10.1090/S0002-9939-1981-0589141-4
- [4] Richard Haydon, Some more characterizations of Banach spaces containing 𝑙₁, Math. Proc. Cambridge Philos. Soc. 80 (1976), no. 2, 269–276. MR 423047, https://doi.org/10.1017/S0305004100052890
- [5] Liliana Janicka, Some measure-theoretical characterization of Banach spaces not containing 𝑙₁, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), no. 7-8, 561–565 (1980) (English, with Russian summary). MR 581552
- [6] Philip W. McCartney, Neighborly bushes and the Radon-Nikodým property for Banach spaces, Pacific J. Math. 87 (1980), no. 1, 157–168. MR 590873
- [7] I. Namioka and R. R. Phelps, Banach spaces which are Asplund spaces, Duke Math. J. 42 (1975), no. 4, 735–750. MR 390721
- [8] Lawrence H. Riddle, Elias Saab, and J. J. Uhl Jr., Sets with the weak Radon-Nikodým property in dual Banach spaces, Indiana Univ. Math. J. 32 (1983), no. 4, 527–541. MR 703283, https://doi.org/10.1512/iumj.1983.32.32038
- [9]
L. H. Riddle and J. J. Uhl, Jr., The fine line between Asplund spaces and spaces not containing a copy of
, preprint.
- [10] Haskell P. Rosenthal, A characterization of Banach spaces containing 𝑙¹, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411–2413. MR 358307, https://doi.org/10.1073/pnas.71.6.2411
- [11]
E. Saab and P. Saab, On Banach spaces not containing
, Pacific J. Math, (to appear).
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B20
Retrieve articles in all journals with MSC: 46B20
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1982-0671210-2
Article copyright:
© Copyright 1982
American Mathematical Society