Displaying similar documents to “Dense strong continuity of mappings and the Radon-Nikodym property.”

Weak compactness and σ-Asplund generated Banach spaces

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...

Weak uniform continuity and weak sequential continuity of continuous n-linear mappings between Banach spaces.

Rajappa K. Asthagiri (1991)

Extracta Mathematicae

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In this paper it is shown that the class L (E,E,...,E;F) of weakly uniformly continuous n-linear mappings from Ex Ex...x E to F on bounded sets coincides with the class L (E,E,...,E;F) of weakly sequentially continuous n-linear mappings if and only if for every Banach space F, each Banach space E for i = 1,2,...,n does not contain a copy of l.