Journal of Inequalities and Applications
Volume 2005 (2005), Issue 4, Pages 435-441
doi:10.1155/JIA.2005.435

Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras

Takeshi Miura,1 Sin-Ei Takahasi,1 and Go Hirasawa2

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.

Abstract

We 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 f from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique ring homomorphism near to f.