An approach to Schreier's space

• Autores: Jesús María Fernández Castillo , Miguel González Velasco
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 6, Nº 2-3, 1991, págs. 166-169
• Idioma: inglés
• Enlaces
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• Resumen

  • 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.