On Supra-Additive and Supra-Multiplicative Maps. (15th September 2013)

• Record Type: Journal Article
• Authors: Chen, Jin Xi; Chen, Zi Li
• Other Names: Xu Gen-Qi Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2013(2013)
• Publication Date: 2013-09-15
• Subjects: Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2013/108535
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : Let A and B be ordered algebras over ℝ, where A has a generating positive cone and B satisfies the property that b 2 > 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.