Orlicz–Lorentz function spaces equipped with the Orlicz norm

We investigate Orlicz–Lorentz function spaces equipped with the Orlicz norm generated by any Orlicz function and any non-increasing weight function. As far as we know, this is the first time such a general research is conducted. First we show some basic properties of the Orlicz norm, including its e...

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Published inRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 117; no. 3
Main Authors Foralewski, Paweł, Kończak, Joanna
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.07.2023
Springer Nature B.V
Subjects
Applications of Mathematics
Characteristic functions
Function space
Infimum
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
Weighting functions
Strict monotonicity
46A80
46B04
Order continuity and copies of
Orlicz norm
46E30
Orlicz–Lorentz spaces
46B20
46B42
Banach symmetric spaces
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Summary:We investigate Orlicz–Lorentz function spaces equipped with the Orlicz norm generated by any Orlicz function and any non-increasing weight function. As far as we know, this is the first time such a general research is conducted. First we show some basic properties of the Orlicz norm, including its equality to the Amemiya norm, the problem of attainability of infimum in the definition of the Amemiya norm and a formula for the norm of a characteristic function. Then we find criteria for the order continuity and strict monotonicity and we study the problem of existence of order linearly isometric copies of l ∞ .
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-023-01449-z