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

100%

Foralewski P., Hudzik H., Kaczmarek R., Krbec M.

Commentationes Mathematicae

2013

tom 53

nr 2

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.

Non-square points of Orlicz-Lorentz function spaces

100%

Kończak J.

Commentationes Mathematicae

2019

tom 59

nr 1-2

In this paper, criteria for non-square points in Orlicz−Lorentz function spaces \(\Lambda_{\varphi, \omega}\) endowed with the Luxemburg norm are given. The widest possible classes of convex Orlicz functions and weight functions are admitted. In consequence, criteria for non-square points in Orlicz spaces \(L^{\varphi}\), which generalize the already known results, are presented.

Ograniczanie wyników

2 Commentationes Mathematicae

1 Foralewski P.

1 Hudzik H.

1 Kaczmarek R.

1 Kończak J.

1 Krbec M.

1 2019

1 2013

Wyniki wyszukiwania

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

Non-square points of Orlicz-Lorentz function spaces