Polynomials on Schreier's space

Details Polynomials on Schreier's space Polynomials on Schreier's space

2000-02-28

arxiv.org/abs/math/0002239v1

Mathematics

Functional Analysis

12 pages

Scientific paper

We introduce a weakened version of the Dunford-Pettis property, and give examples of Banach spaces with this property. In particular, we show that every closed subspace of Schreier's space $S$ enjoys it. As an application, we characterize the weak polynomial convergence of sequences, show that every closed subspace of $S$ has the polynomial Dunford-Pettis property of Bistr\"om et al. and give other polynomial properties of $S$.

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