Journal of Convex Analysis 20 (2013), No. 4, 955--970
Copyright Heldermann Verlag 2013
On the Moduli and Characteristic of Monotonicity in Orlicz-Lorentz Function Spaces
Pawel Foralewski
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland
katon@amu.edu.pl
Henryk Hudzik
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland
hudzik@amu.edu.pl
Radoslaw Kaczmarek
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland
radekk@amu.edu.pl
Miroslav Krbec
Marek Wójtowicz
Institute of Mathematics, Casimir the Great University, Pl. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland
mwojt@ukw.edu.pl
We calculate the characteristic of monotonicity of Orlicz-Lorentz function spaces ΛΦ,ω. Since degenerate Orlicz functions φ and degenerate weight functions ω are also admitted, this investigations concern the most possible wide class of Orlicz-Lorentz function spaces. These results concern both cases - an infinite and a finite non-atomic measure space, although in case of the finite measure the results are much more interesting. Let us recall that calculating of the characteristic of monotonicity of a Banach lattice is of great interest because of the result of A. Betiuk-Pilarska and S. Prus ["Banach lattices which are order uniformly noncreasy", J. Math. Anal. Appl. 342 (2008) 1271-1279] stating that if a Banach lattice X has this characteristic strictly smaller then 1 and X is weakly orthogonal, then it has the weak fixed point property (see W. A. Kirk and B. Sims, "Handbook of metric fixed point theory", Kluwer Academic Publishers (2001)).
Keywords: Banach lattice, Koethe space, Orlicz-Lorentz space, Luxemburg norm, modulus of monotonicity, characteristic of monotonicity, strict monotonicity, uniform monotonicity, weak fixed point property, weak orthogonality.
MSC: 46B42, 46B20, 46A80, 46E30
[ Fulltext-pdf (161 KB)] for subscribers only.