On property $ (\beta) $ in Orlicz spaces

Absract.

In this paper criteria for the property $(\beta)$ in Orlicz function spaces as well as Orlicz sequence spaces are obtained. In the case of the Orlicz function space $L_{\Phi}$ the property $(\beta)$ is equivalent to the uniform convexity of $L_{\Phi}$. In contrast to this result, in Orlicz sequence space $l_{\Phi}$ the property $(\beta)$ is essentially weaker than the uniform convexity of $l_{\Phi}$ and it is equivalent to the reflexivity of $l_{\Phi}$.