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

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.

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Correspondence to Takeshi Miura.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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

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