Extension and lifting of weakly continuous polynomials

Volume 169 / 2005

Raffaella Cilia, Joaquín M. Gutiérrez Studia Mathematica 169 (2005), 229-241 MSC: Primary 46G25; Secondary 46B20, 47H60. DOI: 10.4064/sm169-3-2

Abstract

We show that a Banach space $X$ is an ${\scr L}_1$-space (respectively, an ${\scr L}_\infty$-space) if and only if it has the lifting (respectively, the extension) property for polynomials which are weakly continuous on bounded sets. We also prove that $X$ is an ${\scr L}_1$-space if and only if the space ${\cal P}_{{\rm wb}}(^m\!X)$ of $m$-homogeneous scalar-valued polynomials on $X$ which are weakly continuous on bounded sets is an ${\scr L}_\infty$-space.

Authors

  • Raffaella CiliaDipartimento di Matematica
    Facoltà di Scienze
    Università di Catania
    Viale Andrea Doria 6
    95125 Catania, Italy
    e-mail
  • Joaquín M. GutiérrezDepartamento de Matemática Aplicada
    ETS de Ingenieros Industriales
    Universidad Politécnica de Madrid
    C. José Gutiérrez Abascal 2
    28006 Madrid, Spain
    e-mail

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