On Property $\beta $ of Rolewicz in Köthe–Bochner Function Spaces
Volume 53 / 2005
Bulletin Polish Acad. Sci. Math. 53 (2005), 75-85
MSC: 46E40, 46B20, 46E30.
DOI: 10.4064/ba53-1-7
Abstract
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.
