- Tytuł:
- Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm
- Autorzy:
-
Foralewski, Paweł
Hudzik, Henryk
Kaczmarek, Radosław
Krbec, Miroslav - Powiązania:
- https://bibliotekanauki.pl/articles/746439.pdf
- Data publikacji:
- 2013
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
Orlicz space
Orlicz norm
Kothe space
Kothe dual
characteristic of monotonicity
strict monotonicity
point of order smoothness - Opis:
- We first prove that the property of strict monotonicity of a~K\"othe space \((E,\|.\|_E)\) and\slash or of its K\"othe dual \((E',\|.\|_{E'})\) can be used successfully to compare the supports of \(x\in E\backslash\{\theta\}\) and \(y\in S(E')\), where \(=\|x\|_E\). Next we prove that any element \(x\in S_{+}(E)\) with \(\mu(T\backslash\operatorname{supp} x)=0\) is a~point of order smoothness in \(E\), whenever \(E\) is an order continuous K\"othe space. Finally, we present formulas for the characteristic of monotonicity of Orlicz function spaces endowed with the Orlicz norm in the case when the generating Orlicz function does not satisfy suitable \(\Delta_2\)-condition or the measure is non-atomic infinite, and some lower and upper estimates for the characteristic of monotonicity of this spaces when the measure is non-atomic and finite.
- Źródło:
-
Commentationes Mathematicae; 2013, 53, 2
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł