Polynomials on Schreier's space

2000/02/28 by González, Manuel, Gutiérrez, Joaquín M.
#46B20 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.math/0002239

Abstract

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 Biström et al. and give other polynomial properties of S.

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