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

Lech Drewnowski

Studia Mathematica (1993)

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

Abstract

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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.

How to cite

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Drewnowski, 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

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  1. [1] J. Bourgain, Dunford-Pettis operators on L 1 and the Radon-Nikodym property, Israel J. Math. 37 (1980), 34-47. Zbl0457.46017
  2. [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. [3] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977. 
  4. [4] L. Drewnowski, Another note on copies of l and c 0 in ca(Σ, X), and the equality ca(Σ, X) = cca(Σ, X), preprint, 1990. 
  5. [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. [6] Z. Lipecki, Conditional and simultaneous extensions of group-valued quasi-measures, Glas. Mat. 19 (1984), 49-58. Zbl0598.28018
  7. [7] R. D. Mauldin, Some effects of set-theoretical assumptions in measure theory, Adv. in Math. 27 (1978), 45-62. Zbl0393.28001
  8. [8] A. Michalak, in preparation. 

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