# Polynomial characterizations of the Dunford-Pettis property.

Manuel González; Joaquín M. Gutiérrez

Extracta Mathematicae (1991)

- Volume: 6, Issue: 1, page 17-19
- ISSN: 0213-8743

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topGonzález, 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 -

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