
Journal of Convex Analysis 20 (2013), No. 4, 955970 Copyright Heldermann Verlag 2013 On the Moduli and Characteristic of Monotonicity in OrliczLorentz Function Spaces Pawel Foralewski Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61614 Poznan, Poland katon@amu.edu.pl Henryk Hudzik Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61614 Poznan, Poland hudzik@amu.edu.pl Radoslaw Kaczmarek Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61614 Poznan, Poland radekk@amu.edu.pl Miroslav Krbec Marek Wójtowicz Institute of Mathematics, Casimir the Great University, Pl. Weyssenhoffa 11, 85072 Bydgoszcz, Poland mwojt@ukw.edu.pl We calculate the characteristic of monotonicity of OrliczLorentz function spaces Λ_{Φ,ω}. Since degenerate Orlicz functions φ and degenerate weight functions ω are also admitted, this investigations concern the most possible wide class of OrliczLorentz function spaces. These results concern both cases  an infinite and a finite nonatomic 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. BetiukPilarska and S. Prus ["Banach lattices which are order uniformly noncreasy", J. Math. Anal. Appl. 342 (2008) 12711279] 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, OrliczLorentz space, Luxemburg norm, modulus of monotonicity, characteristic of monotonicity, strict monotonicity, uniform monotonicity, weak fixed point property, weak orthogonality. MSC: 46B42, 46B20, 46A80, 46E30 [ Fulltextpdf (161 KB)] for subscribers only. 