On supra-additive and supra-multiplicative maps

Abstract

Let A and B be ordered algebras over reals, where A has a generating positive cone and B satisfies the property that b2>0 if 0≠bB. 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. © 2013 Jin Xi Chen and Zi Li Chen.