# Nonseparability of the quotient space cabv(∑,m;X)/L¹(m;X) for Banach spaces X without the Radon-Nikodym property

Studia Mathematica (1993)

- Volume: 104, Issue: 2, page 125-132
- ISSN: 0039-3223

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topDrewnowski, Lech. "Nonseparability of the quotient space cabv(∑,m;X)/L¹(m;X) for Banach spaces X without the Radon-Nikodym property." Studia Mathematica 104.2 (1993): 125-132. <http://eudml.org/doc/215964>.

@article{Drewnowski1993,

abstract = {It is shown that if (S,∑,m) is an atomless finite measure space and X is a Banach space without the Radon-Nikodym property, then the quotient space cabv(∑,m;X)/L¹(m;X) is nonseparable.},

author = {Drewnowski, Lech},

journal = {Studia Mathematica},

keywords = {Banach space; spaces of vector measures; Bochner integrable functions; Radon-Nikodym property; nonseparable quotient space; integrable functions},

language = {eng},

number = {2},

pages = {125-132},

title = {Nonseparability of the quotient space cabv(∑,m;X)/L¹(m;X) for Banach spaces X without the Radon-Nikodym property},

url = {http://eudml.org/doc/215964},

volume = {104},

year = {1993},

}

TY - JOUR

AU - Drewnowski, Lech

TI - Nonseparability of the quotient space cabv(∑,m;X)/L¹(m;X) for Banach spaces X without the Radon-Nikodym property

JO - Studia Mathematica

PY - 1993

VL - 104

IS - 2

SP - 125

EP - 132

AB - It is shown that if (S,∑,m) is an atomless finite measure space and X is a Banach space without the Radon-Nikodym property, then the quotient space cabv(∑,m;X)/L¹(m;X) is nonseparable.

LA - eng

KW - Banach space; spaces of vector measures; Bochner integrable functions; Radon-Nikodym property; nonseparable quotient space; integrable functions

UR - http://eudml.org/doc/215964

ER -

## References

top- [1] J. Bourgain, Dunford-Pettis operators on ${L}^{1}$ and the Radon-Nikodym property, Israel J. Math. 37 (1980), 34-47. Zbl0457.46017
- [2] R. D. Bourgin, Geometric Aspects of Convex Sets with the Radon-Nikodým Property, Lecture Notes in Math. 993, Springer, Berlin 1983. Zbl0512.46017
- [3] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977.
- [4] L. Drewnowski, Another note on copies of ${l}_{\infty}$ and ${c}_{0}$ in ca(Σ, X), and the equality ca(Σ, X) = cca(Σ, X), preprint, 1990.
- [5] L. Drewnowski and G. Emmanuele, The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of ${c}_{0}$, this volume, 111-123. Zbl0811.46038
- [6] Z. Lipecki, Conditional and simultaneous extensions of group-valued quasi-measures, Glas. Mat. 19 (1984), 49-58. Zbl0598.28018
- [7] R. D. Mauldin, Some effects of set-theoretical assumptions in measure theory, Adv. in Math. 27 (1978), 45-62. Zbl0393.28001
- [8] A. Michalak, in preparation.

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