On supra-additive and supra-multiplicative maps (Q2443682)

Summary: Let \(A\) and \(B\) be ordered algebras over \(\mathbb R\), where \(A\) has a generating positive cone and \(B\) satisfies the property that \(b^2 > 0\) if \(0 \neq b \in B\). We give some conditions for a map \(T : A \to B\) 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.