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On an extension of norms from a subspace to the whole Banach space keeping their rotundity

100%

Fabian M.

Studia Mathematica

1994-1995

tom 112

nr 3

203-211

Let ℛ denote some kind of rotundity, e.g., the uniform rotundity. Let X admit an ℛ-norm and let Y be a reflexive subspace of X with some ℛ-norm ∥·∥. Then we are able to extend ∥·∥ from Y to an ℛ-norm on X.

Weak compactness and σ-Asplund generated Banach spaces

51%

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.

Ograniczanie wyników

2 Studia Mathematica

2 Fabian M.

1 Montesinos V.

1 Zizler V.

1 2007

1 1995

Wyniki wyszukiwania

On an extension of norms from a subspace to the whole Banach space keeping their rotundity

Weak compactness and σ-Asplund generated Banach spaces