Moduli and characteristics of monotonicity in general Banach lattices and in Orlicz spaces in particular

Some remarks about the moduli of monotonicity are presented. Formulas for the characteristics of monotonicity in Banach lattices are given. Lower and upper estimates of the (lower) modulus of monotonicity of Orlicz spaces equipped with the Luxemburg norm using Simonenko and Lindberg indices as well as some other two parameters for the generated Orlicz function are given. The characteristic of monotonicity ε0,m(LΦ)ε0,m(LΦ) of Orlicz spaces endowed with the Luxemburg norm is estimated from below and another characteristic of monotonicity ε¯0,m(LΦ) of the spaces is computed.