Geodesic
On the Moduli and Characteristic of Monotonicity in Orlicz-Lorentz Function Spaces
Journal of convex analysis, Tome 20 (2013) no. 4, pp. 955-97.

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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)).
Classification : 46B42, 46B20, 46A80, 46E30
Mots-clés : 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 
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     author = {P. Foralewski and H. Hudzik and R. Kaczmarek and M. Krbec and M. W\'ojtowicz},
     title = {On the {Moduli} and {Characteristic} of {Monotonicity} in {Orlicz-Lorentz} {Function} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {955--97},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a4/}
}
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P. Foralewski; H. Hudzik; R. Kaczmarek; M. Krbec; M. Wójtowicz. On the Moduli and Characteristic of Monotonicity in Orlicz-Lorentz Function Spaces. Journal of convex analysis, Tome 20 (2013) no. 4, pp. 955-97. http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a4/