Abstract Riesz* homomorphisms on ordered vector spaces are characterized, intrinsically, via a condition on finite sets. As it is not sufficient to reduce to sets with at most two elements, mild Riesz* homomorphisms (of degree 2) were introduced and investigated. In this paper, we introduce mild Riesz* homomorphisms of higher degrees and generalize the results on mild Riesz* homomorphisms of degree 2 to this setting. We focus on order unit spaces and give sufficient conditions such that mild Riesz* homomorphism of degree n and Riesz* homomorphisms coincide.
Florian Boisen (2026) studied this question.