Displaying similar documents to “A note on the structure of WUR Banach spaces”

A new class of weakly K -analytic Banach spaces

Sophocles Mercourakis, E. Stamati (2006)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we define and investigate a new subclass of those Banach spaces which are K -analytic in their weak topology; we call them strongly weakly K -analytic (SWKA) Banach spaces. The class of SWKA Banach spaces extends the known class of strongly weakly compactly generated (SWCG) Banach spaces (and their subspaces) and it is related to that in the same way as the familiar classes of weakly K -analytic (WKA) and weakly compactly generated (WCG) Banach spaces are related. We show...

w * -basic sequences and reflexivity of Banach spaces

Kamil John (2005)

Czechoslovak Mathematical Journal

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We observe that a separable Banach space X is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if ℒ ( X , Y ) is not reflexive for reflexive X and Y then ℒ ( X 1 , Y ) is is not reflexive for some X 1 ⊂ X , X 1 having a basis.

A note on weakly Lindelöf determined Banach spaces

A. González, Vicente Montesinos (2009)

Czechoslovak Mathematical Journal

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We prove that weakly Lindelöf determined Banach spaces are characterized by the existence of a ``full'' projectional generator. Some other results pertaining to this class of Banach spaces are given.

On some new characterizations of weakly compact sets in Banach spaces

Lixin Cheng, Qingjin Cheng, Zhenghua Luo (2010)

Studia Mathematica

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We show several characterizations of weakly compact sets in Banach spaces. Given a bounded closed convex set C of a Banach space X, the following statements are equivalent: (i) C is weakly compact; (ii) C can be affinely uniformly embedded into a reflexive Banach space; (iii) there exists an equivalent norm on X which has the w2R-property on C; (iv) there is a continuous and w*-lower semicontinuous seminorm p on the dual X* with p ≥ s u p C such that p² is everywhere Fréchet differentiable in...