Weak compactness and σ-Asplund generated Banach spaces

M. Fabian, V. Montesinos, and V. Zizler. "Weak compactness and σ-Asplund generated Banach spaces." Studia Mathematica 181.2 (2007): 125-152. <http://eudml.org/doc/285059>.

@article{M2007,
abstract = {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.},
author = {M. Fabian, V. Montesinos, V. Zizler},
journal = {Studia Mathematica},
keywords = {-Asplund set; -weakly compact set; weakly compactly generated Banach space; -Asplund generated space; Radon-Nikodým compact space},
language = {eng},
number = {2},
pages = {125-152},
title = {Weak compactness and σ-Asplund generated Banach spaces},
url = {http://eudml.org/doc/285059},
volume = {181},
year = {2007},
}

TY - JOUR
AU - M. Fabian
AU - V. Montesinos
AU - V. Zizler
TI - Weak compactness and σ-Asplund generated Banach spaces
JO - Studia Mathematica
PY - 2007
VL - 181
IS - 2
SP - 125
EP - 152
AB - 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.
LA - eng
KW - -Asplund set; -weakly compact set; weakly compactly generated Banach space; -Asplund generated space; Radon-Nikodým compact space
UR - http://eudml.org/doc/285059
ER -