Polynomial characterizations of the Dunford-Pettis property

• Autores: Joaquín M. Gutiérrez, Manuel González Ortiz
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 6, Nº 1, 1991, págs. 17-19
• Idioma: inglés
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• Resumen

  • We introduce and characterize the class Pwd of polynomials between Banach spaces whose restrictions to Dunford-Pettis (DP) sets are weakly continuous. All the weakly compact and the scalar valued polynomials belong to Pwd. We prove that a Banach space E has the Dunford-Pettis (DP) property if and only if every P Î Pwd is weakly sequentially continuous. This result contains a characterization of the DP property given in [3], answering a question of Pelczynski: E has the DP property if and only if any weakly compact polynomial on E takes weak Cauchy sequences into convergent ones. It also extends other characterizations of the DP property by operators to the case of polynomials. Other properties of polynomials between Banach spaces are obtained.