Geodesic
Weak compactness and $\sigma $-Asplund generated Banach spaces
M. Fabian 1   ; V. Montesinos 2   ; V. Zizler 1
1 Mathematical Institute Czech Academy of Sciences Žitná 25 115 67 Praha 1, Czech Republic
2 Departamento de Matemática Aplicada ETSI Telecomunicación Universidad Politécnica de Valencia C//Vera, s//n 46071 Valencia, Spain
Studia Mathematica, Tome 181 (2007) no. 2, pp. 125-152 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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$\sigma$-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 $\sigma$-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.
DOI : 10.4064/sm181-2-2
Keywords: sigma asplund generated banach spaces characterizations subspaces weakly compactly generated spaces prove results radon nikod compacta typically framework weakly lindel determined banach spaces subspaces weakly compactly generated spaces sigma asplund generated spaces purpose study relationships between quantitative versions asplund property dentability differentiability weak compactness banach spaces consequence provide functional analytic proof result arvanitakis compact space eberlein only simultaneously corson quasi radon nikod

M. Fabian  1   ; V. Montesinos  2   ; V. Zizler  1

1 Mathematical Institute Czech Academy of Sciences Žitná 25 115 67 Praha 1, Czech Republic
2 Departamento de Matemática Aplicada ETSI Telecomunicación Universidad Politécnica de Valencia C//Vera, s//n 46071 Valencia, Spain 
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     title = {Weak compactness and $\sigma ${-Asplund} generated {Banach} spaces},
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M. Fabian; V. Montesinos; V. Zizler. Weak compactness and $\sigma $-Asplund generated Banach spaces. Studia Mathematica, Tome 181 (2007) no. 2, pp. 125-152. doi: 10.4064/sm181-2-2

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