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Article: Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras.
- Article from:
- Journal of Inequalities and Applications
- Article date:
- January 1, 2005
- Author:
CopyrightCOPYRIGHT 2005 Hindawi Publishing Corp. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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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.
1. Introduction and statement of results
It seems that the stability problem of functional equations had been first raised by Ulam (cf. [11, Chapter VI] and [12]): For what metric groups G is ...