On property $(\beta )$ of Rolewicz in Köthe–Bochner sequence spaces

Tom 162 / 2004

Henryk Hudzik, Paweł Kolwicz Studia Mathematica 162(2004), 195-212 MSC: 46E40, 46B20, 46E30. DOI: 10.4064/sm162-3-1

Streszczenie

We study property $( \beta ) $ in Köthe–Bochner sequence spaces $E(X)$, where $E$ is any Köthe sequence space and $X$ is an arbitrary Banach space. The question of whether or not this geometric property lifts from $X$ and $E$ to $E(X)$ is examined. We prove that if $\mathop {\rm dim}\nolimits X=\infty $, then $E(X)$ has property $(\beta )$ if and only if $X$ has property $(\beta )$ and $E$ is orthogonally uniformly convex. It is also showed that if $\mathop {\rm dim}\nolimits X<\infty $, then $E(X)$ has property $(\beta )$ if and only if $E$ has property $(\beta )$. Our results essentially extend and improve those from [14] and [15].

Autorzy

  • Henryk HudzikFaculty of Mathematics and Computer Science
    A. Mickiewicz University
    Umultowska 87
    61-614 Poznań, Poland
    e-mail
  • Paweł KolwiczInstitute of Mathematics
    Poznań University of Technology
    Piotrowo 3a
    60-965 Poznań, Poland
    e-mail

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