On the weak star uniformly rotund points of Orlicz spaces (Q1333011)

Let \(x\in S(X)\). The sphere of a Banach space \(x\) is called a weak star uniformly rotund point if \(x_ n\in S(X)\), \(\| x_ n+ x\|\to 2\), implies \(x_ n- x @>{w^*}>> 0\). A space is weak star locally uniformly rotund iff all points of \(S(X)\) are \(W^* UR\) points. The authors give the criterion of \(W^* UR\) point of Orlicz space with Luxemburg norm. For details see \textit{M. A. Krasnosel'skij} and \textit{Ya. B. Rutitskij}, `Convex function and Orlicz spaces', Groningen (1961; Zbl 0095.091 and Zbl 0084.101).