# An approach to Schreier's space.

Jesús M. Fernández Castillo; Manuel González

Extracta Mathematicae (1991)

- Volume: 6, Issue: 2-3, page 166-169
- ISSN: 0213-8743

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topFernández Castillo, Jesús M., and González, Manuel. "An approach to Schreier's space.." Extracta Mathematicae 6.2-3 (1991): 166-169. <http://eudml.org/doc/39945>.

@article{FernándezCastillo1991,

abstract = {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|,where a finite sub-set of natural numbers A = \{n1 < ... < nk\} is said to be admissible if k ≤ n1.In this extract we collect the basic properties of S, which can be considered mainly folklore, and show how this space can be used to provide counter examples to the three-space problem for several properties such as: Dunford-Pettis and Hereditary Dunford-Pettis, weak p-Banach-Saks, and Sp.},

author = {Fernández Castillo, Jesús M., González, Manuel},

journal = {Extracta Mathematicae},

keywords = {Espacios de Banach; Espacios normados; Propiedad de Dunford-Pettis; Problema de tres espacios},

language = {eng},

number = {2-3},

pages = {166-169},

title = {An approach to Schreier's space.},

url = {http://eudml.org/doc/39945},

volume = {6},

year = {1991},

}

TY - JOUR

AU - Fernández Castillo, Jesús M.

AU - González, Manuel

TI - An approach to Schreier's space.

JO - Extracta Mathematicae

PY - 1991

VL - 6

IS - 2-3

SP - 166

EP - 169

AB - 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|,where a finite sub-set of natural numbers A = {n1 < ... < nk} is said to be admissible if k ≤ n1.In this extract we collect the basic properties of S, which can be considered mainly folklore, and show how this space can be used to provide counter examples to the three-space problem for several properties such as: Dunford-Pettis and Hereditary Dunford-Pettis, weak p-Banach-Saks, and Sp.

LA - eng

KW - Espacios de Banach; Espacios normados; Propiedad de Dunford-Pettis; Problema de tres espacios

UR - http://eudml.org/doc/39945

ER -

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