Displaying similar documents to “Extraction of subsequences in Banach spaces.”

An approach to Schreier's space.

Jesús M. Fernández Castillo, Manuel González (1991)

Extracta Mathematicae

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In 1930, J. Schreier [10] introduced the notion of admissibility in order to show that the now called weak-Banach-Saks property does not hold in every Banach space. A variation of this idea produced the Schreier's space (see [1],[2]). This is the space obtained by completion of the space of finite sequences with respect to the following norm: ||x||S = sup(A admissible) ∑j ∈ A |xj|, ...

Biorthogonal systems in Banach spaces

Michael A. Coco (2004)

Studia Mathematica

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We give biorthogonal system characterizations of Banach spaces that fail the Dunford-Pettis property, contain an isomorphic copy of c₀, or fail the hereditary Dunford-Pettis property. We combine this with previous results to show that each infinite-dimensional Banach space has one of three types of biorthogonal systems.

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.

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.