Strict convexity of sequence Orlicz-Musielak spaces with Orlicz norm

AbstractH. Milnes gave in (Pacific J. Math. 18 (1957), 1451–1483) a criterion for strict convexity of Orlicz spaces with respect to the so called Orlicz norm, in the case of nonatomic measure and a usual Young function. Here there are presented necessary and sufficient conditions for strict convexity of Orlicz-Musielak spaces (J. Musielak and W. Orlicz, Studia Math. 18 (1957), 49–65) with Orlicz norm in the case of purely atomic measure. For sequence Orlicz-Musielak spaces with Luxemburg norm, such a criterion is given in (A. Kamińska, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 29 (1981), 137–144)