Displaying similar documents to “Problems concerning weak Asplund spaces”

Complex Banach spaces with Valdivia dual unit ball.

Ondrej F. K. Kalenda (2005)

Extracta Mathematicae

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We study the classes of complex Banach spaces with Valdivia dual unit ball. We give complex analogues of several theorems on real spaces. Further we study relationship of these complex Banach spaces with their real versions and that of real Banach spaces and their complexification. We also formulate several open problems.

On a dual locally uniformly rotund norm on a dual Vašák space

Marián Fabian (1991)

Studia Mathematica

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We transfer a renorming method of transfer, due to G. Godefroy, from weakly compactly generated Banach spaces to Vašák, i.e., weakly K-countably determined Banach spaces. Thus we obtain a new construction of a locally uniformly rotund norm on a Vašák space. A further cultivation of this method yields the new result that every dual Vašák space admits a dual locally uniformly rotund norm.

On some geometric properties concerning closed convex sets.

D. N. Kutzarova, Pei-Kee Lin, P. L. Papini, Xin Tai Yu (1991)

Collectanea Mathematica

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In this article, we consider the (weak) drop property, weak property (a), and property (w) for closed convex sets. Here we give some relations between those properties. Particularly, we prove that C has (weak) property (a) if and only if the subdifferential mapping of Cº is (n-n) (respectively, (n-w)) upper semicontinuous and (weak) compact valued. This gives an extension of a theorem of Giles and the first author.