σ-Asplund generated Banach spaces are used to give new characterizations of subspaces of weakly compactly generated spaces and to prove some results on Radon-Nikodým compacta. We show, typically, that in the framework of weakly Lindelöf determined Banach spaces, subspaces of weakly compactly generated spaces are the same as σ-Asplund generated spaces. For this purpose, we study relationships between quantitative versions of Asplund property, dentability, differentiability, and of weak compactness in Banach spaces. As a consequence, we provide a functional-analytic proof of a result of Arvanitakis: A compact space is Eberlein if (and only if) it is simultaneously Corson and quasi-Radon-Nikodým.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm181-2-2,
author = {M. Fabian and V. Montesinos and V. Zizler},
title = {Weak compactness and $\sigma$-Asplund generated Banach spaces},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {125-152},
zbl = {1127.46003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm181-2-2}
}
M. Fabian; V. Montesinos; V. Zizler. Weak compactness and σ-Asplund generated Banach spaces. Studia Mathematica, Tome 178 (2007) pp. 125-152. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm181-2-2/