On the Moduli and Characteristic of Monotonicity in Orlicz-Lorentz Function Spaces

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)).