On Property $\beta $ of Rolewicz in Köthe–Bochner Function Spaces

Volume 53 / 2005

Paweł Kolwicz Bulletin Polish Acad. Sci. Math. 53 (2005), 75-85 MSC: 46E40, 46B20, 46E30. DOI: 10.4064/ba53-1-7


It is proved that the Köthe–Bochner function space $E(X)$ has property $\boldsymbol{\beta }$ if and only if $X$ is uniformly convex and $E$ has property $\boldsymbol{\beta }$. In particular, property $\boldsymbol{\beta }$ does not lift from $X$ to $E( X) $ in contrast to the case of Köthe–Bochner sequence spaces.


  • Paweł KolwiczInstitute of Mathematics
    Electrical Engineering Faculty
    University of Technology
    Piotrowo 3a
    60-965 Poznań, Poland

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