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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 48, Pages 3025-3029
http://dx.doi.org/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 Hindawi Publishing Corporation. 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:AB, 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.