On Supra-Additive and Supra-Multiplicative Maps

Abstract EN

Let A and B be ordered algebras over ℝ, where A has a generating positive cone and B satisfies the property that b2>0 if 0≠b∈B.

We give some conditions for a map T:A→B which is supra-additive and supra-multiplicative for all positive and negative elements to be linear and multiplicative; that is, T is a homomorphism of algebras.

Our results generalize some known results on supra-additive and supra-multiplicative maps between spaces of real functions.