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

Paweł Foralewski, et al. "Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm." Commentationes Mathematicae 53.2 (2013): null. <http://eudml.org/doc/292394>.

@article{PawełForalewski2013,
abstract = {We first prove that the property of strict monotonicity of a Köthe space $(E,\Vert .\Vert _E)$ and/or of its Köthe dual $(E^\{\prime \},\Vert .\Vert _\{E^\{\prime \}\})$ can be used successfully to compare the supports of $x\in E\backslash \lbrace \theta \rbrace $ and $y\in S(E^\{\prime \})$, where $=\Vert x\Vert _E$. 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 Köthe 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.},
author = {Paweł Foralewski, Henryk Hudzik, Radosław Kaczmarek, Miroslav Krbec},
journal = {Commentationes Mathematicae},
keywords = {Orlicz space; Orlicz norm; Kothe space; Kothe dual; characteristic of monotonicity; strict monotonicity; point of order smoothness},
language = {eng},
number = {2},
pages = {null},
title = {Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm},
url = {http://eudml.org/doc/292394},
volume = {53},
year = {2013},
}

TY - JOUR
AU - Paweł Foralewski
AU - Henryk Hudzik
AU - Radosław Kaczmarek
AU - Miroslav Krbec
TI - Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm
JO - Commentationes Mathematicae
PY - 2013
VL - 53
IS - 2
SP - null
AB - We first prove that the property of strict monotonicity of a Köthe space $(E,\Vert .\Vert _E)$ and/or of its Köthe dual $(E^{\prime },\Vert .\Vert _{E^{\prime }})$ can be used successfully to compare the supports of $x\in E\backslash \lbrace \theta \rbrace $ and $y\in S(E^{\prime })$, where $=\Vert x\Vert _E$. 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 Köthe 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.
LA - eng
KW - Orlicz space; Orlicz norm; Kothe space; Kothe dual; characteristic of monotonicity; strict monotonicity; point of order smoothness
UR - http://eudml.org/doc/292394
ER -