Smooth renormings of the Lebesgue–Bochner function space $L^1(\mu ,X)$

Tom 209 / 2012

Marián Fabian, Sebastián Lajara Studia Mathematica 209 (2012), 247-265 MSC: 46B03, 46B20, 46E40. DOI: 10.4064/sm209-3-4

Streszczenie

We show that, if $\mu$ is a probability measure and $X$ is a Banach space, then the space $L^1(\mu,X)$ of Bochner integrable functions admits an equivalent Gâteaux (or uniformly Gâteaux) smooth norm provided that $X$ has such a norm, and that if $X$ admits an equivalent Fréchet (resp. uniformly Fréchet) smooth norm, then $L^1(\mu,X)$ has an equivalent renorming whose restriction to every reflexive subspace is Fréchet (resp. uniformly Fréchet) smooth.

Autorzy

  • Marián FabianInstitute of Mathematics
    Czech Academy of Sciences
    Žitná 25
    115 67 Praha 1, Czech Republic
    e-mail
  • Sebastián LajaraDepartamento de Matemáticas
    Escuela de Ingenieros Industriales
    Universidad de Castilla-La Mancha
    Campus Universitario
    02071 Albacete, Spain
    e-mail

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