On property $(\beta) $ of Rolewicz in Musielak-Orlicz sequencespaces equipped with the Orlicz norm
Volume 68 / 2005
Banach Center Publications 68 (2005), 79-86
MSC: 46B20, 46A45, 46B45.
DOI: 10.4064/bc68-0-9
Abstract
We prove that the Musielak-Orlicz sequence space with the Orlicz norm has property $(\beta) $ iff it is reflexive. It is a generalization and essential extension of the respective results from \cite{chp} and \cite {beta-orlicz}. Moreover, taking an arbitrary Musielak-Orlicz function instead of an $N$-function we develop new methods and techniques of proof and we consider a wider class of spaces than in \cite{chp} and \cite{beta-orlicz}.
