On the \(WM\) points of Orlicz function spaces endowed with Orlicz norm (Q1922173)

In 1975, B. B. Pander and O. P. Kappor introduced the WM property. For a Banach space \(X\), let \(B(X)\), \(S(X)\) be the unit ball and unit sphere of \(X\), respectively. \(x\in S(X)\) is called a WM point if \(x_n\in B(X)\), \(|x_n+x|\to 2\) imply that there is a supporting functional \(f\) of \(x\), satisfying \(f(x_n)\to 1\). If all points of \(S(X)\) are WM points, then \(X\) has the WM property. In this paper, a criterion of WM point in Orlicz function spaces endowed with Orlicz norm and a sufficient and necessary condition that \(X\) has the WM property are given. The descriptions and proofs about the theorem in this paper are rather complicated.