A stronger Dunford–Pettis property

Volume 184 / 2008

H. Carrión, P. Galindo, M. L. Lourenço Studia Mathematica 184 (2008), 205-216 MSC: Primary 46B20; Secondary 46G20. DOI: 10.4064/sm184-3-1

Abstract

We discuss a strong version of the Dunford–Pettis property, earlier named $(DP^*)$ property, which is shared by both $\ell _1$ and $\ell _\infty .$ It is equivalent to the Dunford–Pettis property plus the fact that every quotient map onto $c_0$ is completely continuous. Other weak sequential continuity results on polynomials and analytic mappings related to the $(DP^*)$ property are shown.

Authors

  • H. CarriónDepartamento de Matemática
    Instituto de Matemática e Estatística
    Universidade de São Paulo
    Caixa Postal 66281
    CEP 05315-970, São Paulo, Brazil
    e-mail
  • P. GalindoDepartamento de Análisis Matemático
    Facultad de Matemáticas
    Universidad de Valencia
    46100 Burjasot (Valencia), Spain
    e-mail
  • M. L. LourençoDepartamento de Matemática
    Instituto de Matemática e Estatística
    Universidade de São Paulo
    Caixa Postal 66281
    CEP 05315-970, São Paulo, Brazil
    e-mail

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