International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 48, Pages 3025-3029
doi:10.1155/S0161171203302352

Ring homomorphisms on real Banach algebras

Takeshi Miura and Sin-Ei Takahasi

 Department of Basic Technology, Faculty of Engineering, Yamagata University, Yonezawa 992-8510, Japan
Received 26 February 2003

Abstract

Let B be a strictly real commutative real Banach algebra with the carrier space ΦB. If A is a commutative real Banach algebra, then we give a representation of a ring homomorphism ρ:A→B, which needs not be linear nor continuous. If A is a commutative complex Banach algebra, then ρ(A) is contained in the radical of B.