On non-midpoint locally uniformly rotund normability in Banach spaces.

Mirmostafaee, A.K.

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Displaying similar documents to “On non-midpoint locally uniformly rotund normability in Banach spaces.”

A note on the structure of WUR Banach spaces

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Commentationes Mathematicae Universitatis Carolinae

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We present an example of a Banach space $E$ admitting an equivalent weakly uniformly rotund norm and such that there is no $Φ : E \to c_{0} (Γ)$ , for any set $Γ$ , linear, one-to-one and bounded. This answers a problem posed by Fabian, Godefroy, Hájek and Zizler. The space $E$ is actually the dual space $Y^{*}$ of a space $Y$ which is a subspace of a WCG space.

Banach-Mackey spaces.

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On locally uniformly convex and differentiable norms in certain non-separable Banach spaces

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On super-weakly compact sets and uniformly convexifiable sets

Lixin Cheng, Qingjin Cheng, Bo Wang, Wen Zhang (2010)

Studia Mathematica

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This paper mainly concerns the topological nature of uniformly convexifiable sets in general Banach spaces: A sufficient and necessary condition for a bounded closed convex set C of a Banach space X to be uniformly convexifiable (i.e. there exists an equivalent norm on X which is uniformly convex on C) is that the set C is super-weakly compact, which is defined using a generalization of finite representability. The proofs use appropriate versions of classical theorems, such as James'...

On weakly locally uniformly rotund norms which are not locally uniformly rotund

Szymon Draga (2015)

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We show that every infinite-dimensional Banach space with separable dual admits an equivalent norm which is weakly locally uniformly rotund but not locally uniformly rotund.

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Michal Johanis (2009)

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The notion of functions dependent locally on finitely many coordinates plays an important role in the theory of smoothness and renormings on Banach spaces, especially when higher order smoothness is involved. In this note we investigate the structural properties of Banach spaces admitting (arbitrary) bump functions depending locally on finitely many coordinates.