The Radon--Nikodym theorem for reflexive Banach spaces.
Bárcenas, Diómedes (2003)
Divulgaciones Matemáticas
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Bárcenas, Diómedes (2003)
Divulgaciones Matemáticas
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Marián J. Fabián, Martin Heisler, Eva Matoušková (1998)
Commentationes Mathematicae Universitatis Carolinae
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A family of compact spaces containing continuous images of Radon-Nikod’ym compacta is introduced and studied. A family of Banach spaces containing subspaces of Asplund generated (i.e., GSG) spaces is introduced and studied. Further, for a continuous image of a Radon-Nikod’ym compact we prove: If is totally disconnected, then it is Radon-Nikod’ym compact. If is adequate, then it is even Eberlein compact.
Charles Stegall (1994)
Acta Universitatis Carolinae. Mathematica et Physica
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J. Orihuela, W. Schachermayer, M. Valdivia (1991)
Studia Mathematica
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N. Tomczak-Jaegermann (1981)
Colloquium Mathematicae
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Ch. Stegall (1975-1976)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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Luis Oncina (2001)
Studia Mathematica
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We give a sufficient and necessary condition for a Radon-Nikodým compact space to be Eberlein compact in terms of a separable fibre connecting weak-* and norm approximation.
W. J. Davis (1973-1974)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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Lech Drewnowski (1993)
Studia Mathematica
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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.
Pradipta Bandyopadhyay, Bor-Luh Lin, T. S. S. R. K. Rao (2009)
Colloquium Mathematicae
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We study Banach spaces X with subspaces Y whose unit ball is densely remotal in X. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set E ⊆ X, the set of Bochner integrable functions with values in E is a remotal set in L¹(μ,X). ...
V. Farmaki (1986)
Studia Mathematica
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M. Fabian, V. Montesinos, V. Zizler (2007)
Studia Mathematica
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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...