Polynomial characterizations of the Dunford-Pettis property.

González, Manuel, and Gutiérrez, Joaquín M.. "Polynomial characterizations of the Dunford-Pettis property.." Extracta Mathematicae 6.1 (1991): 17-19. <http://eudml.org/doc/39908>.

@article{González1991,
abstract = {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 ∈ 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.},
author = {González, Manuel, Gutiérrez, Joaquín M.},
journal = {Extracta Mathematicae},
keywords = {Propiedad de Dunford-Pettis; Espacios de Banach; Espacios métricos; Aproximación polinómica},
language = {eng},
number = {1},
pages = {17-19},
title = {Polynomial characterizations of the Dunford-Pettis property.},
url = {http://eudml.org/doc/39908},
volume = {6},
year = {1991},
}

TY - JOUR
AU - González, Manuel
AU - Gutiérrez, Joaquín M.
TI - Polynomial characterizations of the Dunford-Pettis property.
JO - Extracta Mathematicae
PY - 1991
VL - 6
IS - 1
SP - 17
EP - 19
AB - 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 ∈ 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.
LA - eng
KW - Propiedad de Dunford-Pettis; Espacios de Banach; Espacios métricos; Aproximación polinómica
UR - http://eudml.org/doc/39908
ER -