Título inglés | An approach to Schreier's space. |
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Título español | Una aproximación al espacio de Schreier. |
Autor/es | Fernández Castillo, Jesús M. ; González, Manuel |
Organización | Dep. Mat. Univ. Extremadura, Badajoz, España;Dep. Mat Univ. Cantabria, Santander, España |
Revista | 0213-8743 |
Publicación | 1991, 6 (2-3): 166-169, 10 Ref. |
Tipo de documento | articulo |
Idioma | Inglés |
Resumen inglés | 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 Î 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. |
Clasificación UNESCO | 120203 |
Palabras clave español | Espacios de Banach ; Espacios normados ; Propiedad de Dunford-Pettis ; Problema de tres espacios |
Código MathReviews | MR1185369 |
Acceso al artículo completo |