Geodesic
On Property $\beta $ of Rolewicz in Köthe–Bochner Function Spaces
Paweł Kolwicz1
1 Institute of Mathematics Electrical Engineering Faculty University of Technology Piotrowo 3a 60-965 Poznań, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 1, pp. 75-85

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ba53-1-7
Keywords: proved bochner function space has property boldsymbol beta only uniformly convex has property boldsymbol beta particular property boldsymbol beta does lift contrast bochner sequence spaces

Paweł Kolwicz 1

1 Institute of Mathematics Electrical Engineering Faculty University of Technology Piotrowo 3a 60-965 Poznań, Poland 
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Paweł Kolwicz. On Property $\beta $ of Rolewicz in Köthe–Bochner Function Spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 1, pp. 75-85. doi: 10.4064/ba53-1-7

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