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2012•Communications of the Korean Mathematical SocietyOpen access

JORDAN *-HOMOMORPHISMS BETWEEN UNITAL C*-ALGEBRAS

M‎. ‎Eshaghi Gordji, N. Ghobadipour, Choon-Kil Park

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Abstract

In this paper, we prove the superstability and the generalized Hyers-Ulam stability of Jordan *-homomorphisms between unital $C^*$ -algebras associated with the following functional equation $$f(\frac{-x+y}{3})+f(\frac{x-3z}{c})+f(\frac{3x-y+3z}{3})=f(x)$$ . Morever, we investigate Jordan *-homomorphisms between unital $C^*$ -algebras associated with the following functional inequality $${\parallel}f(\frac{-x+y}{3})+f(\frac{x-3z}{3})+f(\frac{3x-y+3z}{3}){\parallel}\leq{\parallel}f(x)\parallel$$ .

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In this paper, we prove the superstability and the generalized Hyers-Ulam stability of Jordan *-homomorphisms between unital $C^*$ -algebras associated with the following functional equation $$f(\frac{-x+y}{3})+f(\frac{x-3z}{c})+f(\frac{3x-y+3z}{3})=f(x)$$ . Morever, we investigate Jordan *-homomorphisms between unital $C^*$ -algebras associated with the following functional inequality $${\parallel}f(\frac{-x+y}{3})+f(\frac{x-3z}{3})+f(\frac{3x-y+3z}{3}){\parallel}\leq{\parallel}f(x)\parallel$$ .

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Available abstract

In this paper, we prove the superstability and the generalized Hyers-Ulam stability of Jordan *-homomorphisms between unital $C^*$ -algebras associated with the following functional equation $$f(\frac{-x+y}{3})+f(\frac{x-3z}{c})+f(\frac{3x-y+3z}{3})=f(x)$$ . Morever, we investigate Jordan *-homomorphisms between unital $C^*$ -algebras associated with the following functional inequality $${\parallel}f(\frac{-x+y}{3})+f(\frac{x-3z}{3})+f(\frac{3x-y+3z}{3}){\parallel}\leq{\parallel}f(x)\parallel$$ .

Key concepts: Homomorphism, Unital, Mathematics, Combinatorics, Algebra over a field, Pure mathematics

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