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https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56414
2014-03-14T10:41:09Z
Collectanea Mathematica
1997: Vol.: 48 Núm.: 4 -6; 587-600
$P$-convexity of Musielak-Orlicz sequence spaces of Bochner type
Kolwicz, Pawel
Pluciennik, Ryszard
1997-01-13 00:00:00
url:https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56414
eng
It is proved that the Musielak-Orlicz sequence space $l_\varphi(X)$ of Bochner type is $\texttt{P}$-convex if and only if both spaces $l_\varphi(\mathbb{R})$ and $X$ are $\texttt{P}$-convex. In particular, the Lebesgue-Bochner sequence space $l^p(X)$ is $\texttt{P}$-convex if $X$ is $\texttt{P}$-convex and $1 < p <\infty$.