Displaying similar documents to “Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms”

Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis

Rychter, Jan (2000)

Serdica Mathematical Journal

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*Supported in part by GAˇ CR 201-98-1449 and AV 101 9003. This paper is based on a part of the author’s MSc thesis written under the supervison of Professor V. Zizler. It is shown that a Banach space X admits an equivalent uniformly Gateaux differentiable norm if it has an unconditional basis and X* admits an equivalent norm which is uniformly rotund in every direction.

Weakly uniformly rotund Banach spaces

Aníbal Moltó, Vicente Montesinos, José Orihuela, Stanimir L. Troyanski (1998)

Commentationes Mathematicae Universitatis Carolinae

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The dual space of a WUR Banach space is weakly K-analytic.

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'...