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
Department of Basic Technology, Faculty of Engineering, Yamagata University, Yonezawa 992-8510, Japan
Received 26 February 2003
Copyright © 2003 Takeshi Miura and Sin-Ei Takahasi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.