Open Access

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

Journal of Inequalities and Applications20052005:735242

https://doi.org/10.1155/JIA.2005.435

Received: 18 July 2003

Published: 31 August 2005

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

Authors’ Affiliations

(1)
Department of Basic Technology, Applied Mathematics and Physics, Yamagata University
(2)
Department of Mathematics, Nippon Institute of Technology

Copyright

© Miura et al. 2005