Complex convexity of Musielak-Orlicz function spaces equipped with the \(p\)-Amemiya norm (Q1722315)

Summary: The complex convexity of Musielak-Orlicz function spaces equipped with the \(p\)-Amemiya norm is mainly discussed. It is obtained that, for any Musielak-Orlicz function space equipped with the \(p\)-Amemiya norm when \(1 \leq p < \infty\), complex strongly extreme points of the unit ball coincide with complex extreme points of the unit ball. Moreover, criteria for them in above spaces are given. Criteria for complex strict convexity and complex midpoint locally uniform convexity of above spaces are also deduced.