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

摘要

In this paper we calculate the characteristic of monotonicity of Orlicz-Lorentz function spaces Λ_(Φ,ω.) Since degenerate Orlicz functions φ and degenerate weight functions ω are also admitted, the 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 Betiuk-Pilarska and Prus [2] 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 [29]).