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Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras
Journal of Inequalities and Applications volume 2005, Article number: 735242 (2005)
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.
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Miura, T., Takahasi, SE. & Hirasawa, G. Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras. J Inequal Appl 2005, 735242 (2005). https://doi.org/10.1155/JIA.2005.435