Weak compactness and σ-Asplund generated Banach spaces

• Autorzy: M. Fabian , V. Montesinos , V. Zizler
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B50: Compactness in Banach (or normed) spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 181
• Numer: 2
• Strony: 125-152

Daty

wydano

2007

Twórcy

autor

M. Fabian

• Mathematical Institute, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic

autor

V. Montesinos

• Departamento de Matemática Aplicada, ETSI Telecomunicación, Universidad Politécnica de Valencia, C/Vera, s/n, 46071 Valencia, Spain

autor

V. Zizler

• Mathematical Institute, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic

Identyfikatory

DOI

10.4064/sm181-2-2