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

top
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

top

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

top
  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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.