Displaying similar documents to “Weakly uniformly rotund 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...

Remarks on the weak-polynomial convergence on a Banach space.

Jesús A. Jaramillo, Angeles Prieto Yerro (1991)

Extracta Mathematicae

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We shall be concerned in this note with some questions posed by Carne, Cole and Gamelin in [3], involving the weak-polynomial convergence and its relation to the tightness of certain algebras of analytic functions on a Banach space.

Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms

Fabian, Marián, Hájek, Petr, Zizler, Václav (1997)

Serdica Mathematical Journal

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* Supported by grants: AV ĈR 101-95-02, GAĈR 201-94-0069 (Czech Republic) and NSERC 7926 (Canada). It is shown that the dual unit ball BX∗ of a Banach space X∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a uniformly Gâteaux smooth norm and X is a subspace of a weakly compactly generated space. The bidual unit ball BX∗∗ of a Banach space X∗∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a weakly uniformly...

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...

The b -weak compactness of weak Banach-Saks operators

Belmesnaoui Aqzzouz, Othman Aboutafail, Taib Belghiti, Jawad H'michane (2013)

Mathematica Bohemica

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We characterize Banach lattices on which every weak Banach-Saks operator is b-weakly compact.