Multiplication Operators on Generalized Orlicz Spaces Associated to Banach Function Spaces

Aris B., Öztop S., Tabatabaie S. M., Uysal B. H., Üster R.

IRANIAN JOURNAL OF SCIENCE, cilt.48, sa.6, ss.1489-1497, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 6
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s40995-024-01723-8
  • Dergi Adı: IRANIAN JOURNAL OF SCIENCE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
  • Sayfa Sayıları: ss.1489-1497
  • Anahtar Kelimeler: 46E30, Banach function space, Compact operator, Essential norm, Multiplication operator, Orlicz space, Solidity, Young function
  • İstanbul Üniversitesi Adresli: Evet

Özet

In this paper, we study multiplication operators on generalized Orlicz spaces X Phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X<^>\Phi$$\end{document} associated to a Banach function space X, where Phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi$$\end{document} is a Young function, and give some characterization of them to be well-defined and bounded. Also, we present some sufficient and necessary conditions for such operators to be compact or invertible. Moreover, we find the essential norm of a multiplication operator on X Phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X<^>\Phi$$\end{document} while the context measure space is discrete. Many results of this paper cover known Banach function spaces related to Orlicz one.