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Weak compactness and σ-Asplund generated Banach spaces

100%

Fabian M., Montesinos V., Zizler V.

Studia Mathematica

2007

tom 181

nr 2

125-152

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.

Solution to a problem of S. Rolewicz

50%

Montesinos V.

Studia Mathematica

1985

tom 81

nr 1

65-69

Drop property equals reflexivity

50%

Montesinos V.

Studia Mathematica

1987

tom 87

nr 1

93-100

Ograniczanie wyników

3 Studia Mathematica

3 Montesinos V.

1 Fabian M.

1 Zizler V.

1 2007

1 1987

1 1985

Wyniki wyszukiwania

Weak compactness and σ-Asplund generated Banach spaces

Solution to a problem of S. Rolewicz

Drop property equals reflexivity