Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm

• Autorzy: Paweł Foralewski , Henryk Hudzik , Radosław Kaczmarek , Miroslav Krbec
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Orlicz space; Orlicz norm; Kothe space; Kothe dual; characteristic of monotonicity; strict monotonicity; point of order smoothness

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2013
• Tom: 53
• Numer: 2

Daty

wydano

2013

online

2017-04-08

Twórcy

autor

Paweł Foralewski

autor

Henryk Hudzik

autor

Radosław Kaczmarek

autor

Miroslav Krbec

Identyfikatory

DOI

10.14708/cm.v53i2.4365