Multiplication Operators on Weighted Grand Lorentz Spaces with Various Properties

Eryılmaz İ.

WSEAS Transactions on Mathematics, vol.22, pp.271-278, 2023 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 22
  • Publication Date: 2023
  • Doi Number: 10.37394/23206.2023.22.32
  • Journal Name: WSEAS Transactions on Mathematics
  • Journal Indexes: Scopus, INSPEC, zbMATH
  • Page Numbers: pp.271-278
  • Keywords: Compact operator, Multiplication operator, Weighted Grand Lorentz space
  • Ondokuz Mayıs University Affiliated: Yes


- The concept of Lebesgue space has been generalized to the grand Lebesgue space with non-weight and weight, and the classical Lorentz space concept has been generalized to grand Lorentz spaces with a similar logic. In this study, instead of using rearrangement for a measurable function, weighted Grand Lorentz spaces are defined by using the maximal function 1 ≤ p, q ≤ ∞ where the weight function is measurable, complex valued, and locally bounded. In addition, multiplication operators on weighted grand Lorentz spaces are defined and the fundamental properties of these operators such as boundedness, closed range, invertibility, compactness, and closedness are characterized.