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 \( l_{\Phi} \).
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Received: 1.12.1995; new version received 9.8.1996.
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Cui, Y., Płuciennik, R. & Wang, T. On property $ (\beta) $ in Orlicz spaces. Arch. Math. 69, 57–69 (1997). https://doi.org/10.1007/s000130050093
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DOI: https://doi.org/10.1007/s000130050093