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

Studia Mathematica (1996)

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

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topLópez, 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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- [7] D. van Dulst, Characterizations of Banach Spaces not Containing ${l}^{1}$, CWI Tract 59, Stichting Math. Centrum, Amsterdam, 1989.
- [8] R. C. James, Some interesting Banach spaces, Rocky Mountain J. Math. 23 (1993), 911-937. Zbl0797.46010
- [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] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Ergeb. Math. Grenzgeb. 92, Springer, 1977. Zbl0362.46013
- [11] R. R. Phelps, Dentability and extreme points in Banach spaces, J. Funct. Anal. 17 (1974), 78-90. Zbl0287.46026
- [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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