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

Basar E., ÖZTOP KAPTANOĞLU S., UYSAL B. H., Yasar S.

MATHEMATISCHE NACHRICHTEN, vol.296, no.11, pp.5042-5062, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 296 Issue: 11
  • Publication Date: 2023
  • Doi Number: 10.1002/mana.202200374
  • Journal Name: MATHEMATISCHE NACHRICHTEN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.5042-5062
  • Istanbul University Affiliated: Yes

Abstract

Let Phi be an Orlicz function and L-Phi(X, Sigma, mu) be the corresponding Orlicz space on a non-atomic, sigma-finite, complete measure space (X,Sigma, mu). We describe the extreme points of unit ball of Orlicz spaces equipped with the sigma-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..-norms with respect to a constant.