We deal with additive m
onot
one mappings defined
on a lattice-ordered Abelian group and having values in a Dedekind complete Riesz
space and which are invariant with respect to some representati
on of an amenable semigroup. Using a Hahn-
Banach-type theorem of Zbigniew Gajda, we obtain generalizati
ons of factorizati
on theorems obtained in 1984 by Wolfgang Arendt for positive linear operators. The theorems of Arendt are generalized in two directi
ons. First, we extend these results from the case of linear operators
acting between Riesz
spaces to the case of additive mappings between lattice-ordered Abelian
groups. Sec
ond, we study mappings which are invariant with respect to a semigroup representati
on.
As an application of the results obtained, we show some property of composition operators between spaces of additive functions acting between lattice-ordered groups.
