Year: 2000
Type: preprint
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 $S$.
Source: arXiv (Cornell University)
Authors: González, Manuel, Gutiérrez, Joaquín M.
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951346685