Journal of Inequalities and Applications
Volume 2005 (2005), Issue 4, Pages 435-441
Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras
1Department of Basic Technology, Applied Mathematics and Physics, Yamagata University, Yonezawa 992-8510, Japan
2Department of Mathematics, Nippon Institute of Technology, Miyashiro, Saitama 345-8501, Japan
Received 18 July 2003
Copyright © 2005 Takeshi Miura et al. 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.
AbstractWe prove that a Jordan homomorphism from a Banach algebra into a
semisimple commutative Banach algebra is a ring homomorphism.
Using a signum effectively, we can give a simple proof of the
Hyers-Ulam-Rassias stability of a Jordan homomorphism between
Banach algebras. As a direct corollary, we show that to each
approximate Jordan homomorphism from a Banach algebra into a
semisimple commutative Banach algebra there corresponds a unique
ring homomorphism near to .