# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

### Tom 162 / 2004

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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