Extreme points in Orlicz spaces equipped with s‐norms and closedness

Abstract

Let Φ be an Orlicz function and 𝐿 Φ (𝑋, Σ, 𝜇) be the corresponding Orlicz space on a non-atomic, 𝜎-finite, complete measure space (𝑋, Σ, 𝜇). We describe the extreme points of unit ball of Orlicz spaces equipped with the 𝑠-norm. We also investigate the closedness of the set of extreme points of unit ball. Our study generalizes and unifies the results that have been obtained for the Orlicz norm, the Luxemburg norm and the 𝑝-Amemiya norm separately. We further classify the outer functions that generate 𝑠-norms with respect to a constant.