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RNP and KMP are equivalent for some Banach spaces with shrinking basis

Ginés López; Juan Mena

Studia Mathematica (1996)

  • Volume: 118, Issue: 1, page 11-17
  • ISSN: 0039-3223

Abstract

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We get a characterization of PCP in Banach spaces with shrinking basis. Also, we prove that the Radon-Nikodym and Krein-Milman properties are equivalent for closed, convex and bounded subsets of some Banach spaces with shrinking basis.

How to cite

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López, Ginés, and Mena, Juan. "RNP and KMP are equivalent for some Banach spaces with shrinking basis." Studia Mathematica 118.1 (1996): 11-17. <http://eudml.org/doc/216258>.

@article{López1996,
abstract = {We get a characterization of PCP in Banach spaces with shrinking basis. Also, we prove that the Radon-Nikodym and Krein-Milman properties are equivalent for closed, convex and bounded subsets of some Banach spaces with shrinking basis.},
author = {López, Ginés, Mena, Juan},
journal = {Studia Mathematica},
keywords = {Banach spaces with shrinking basis; Radon-Nikodym and Krein-Milman properties are equivalent},
language = {eng},
number = {1},
pages = {11-17},
title = {RNP and KMP are equivalent for some Banach spaces with shrinking basis},
url = {http://eudml.org/doc/216258},
volume = {118},
year = {1996},
}

TY - JOUR
AU - López, Ginés
AU - Mena, Juan
TI - RNP and KMP are equivalent for some Banach spaces with shrinking basis
JO - Studia Mathematica
PY - 1996
VL - 118
IS - 1
SP - 11
EP - 17
AB - We get a characterization of PCP in Banach spaces with shrinking basis. Also, we prove that the Radon-Nikodym and Krein-Milman properties are equivalent for closed, convex and bounded subsets of some Banach spaces with shrinking basis.
LA - eng
KW - Banach spaces with shrinking basis; Radon-Nikodym and Krein-Milman properties are equivalent
UR - http://eudml.org/doc/216258
ER -

References

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  1. [1] S. Argyros, E. Odell and H. Rosenthal, On certain convex subsets of c 0 , in: Lecture Notes in Math. 1332, Springer, Berlin, 1988, 80-111. 
  2. [2] J. Bourgain, La propriété de Radon-Nikodym, Publ. Math. Univ. Pierre et Marie Curie 36, 1979. 
  3. [3] J. Bourgain and H. Rosenthal, Geometrical implications of certain finite-dimensional decompositions, Bull. Soc. Math. Belg. Sér. B 32 (1980), 57-82. Zbl0463.46011
  4. [4] R. D. Bourgin, Geometric Aspects of Convex Sets with the Radon-Nikodým Property, Lecture Notes in Math. 993, Springer, 1980. Zbl0512.46017
  5. [5] J. Diestel and J. J. Uhl., Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1977. 
  6. [6] D. van Dulst, Reflexive and Superreflexive Banach Spaces, Math. Centre Tracts 102, Math. Centrum, Amsterdam, 1978. Zbl0412.46006
  7. [7] D. van Dulst, Characterizations of Banach Spaces not Containing l 1 , CWI Tract 59, Stichting Math. Centrum, Amsterdam, 1989. 
  8. [8] R. C. James, Some interesting Banach spaces, Rocky Mountain J. Math. 23 (1993), 911-937. Zbl0797.46010
  9. [9] J. Lindenstrauss and C. Stegall, Examples of separable spaces which do not contain l 1 and whose duals are non-separable, Studia Math. 54 (1975), 81-105. Zbl0324.46017
  10. [10] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Ergeb. Math. Grenzgeb. 92, Springer, 1977. Zbl0362.46013
  11. [11] R. R. Phelps, Dentability and extreme points in Banach spaces, J. Funct. Anal. 17 (1974), 78-90. Zbl0287.46026
  12. [12] W. Schachermayer, The Radon-Nikodym property and the Krein-Milman property are equivalent for strongly regular sets, Trans. Amer. Math. Soc. 303 (1987), 673-687. Zbl0633.46023

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