Monotonicities in Orlicz Spaces Equipped with Mazur-Orlicz F-Norm

Abstract EN

Some basic properties in Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz F-norm are studied in this paper.

We give some relationships between the modulus and the Mazur-Orlicz F-norm.

We obtain an interesting result that the norm of an element in line segments is formed by two elements on the unit sphere less than or equal to 1 if and only if that the monotone function is a convex function.

The criterion that Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz F-norm are strictly monotone or lower locally uniform monotone is presented.