Jordan ∗−homomorphisms between unital C∗−algebras
نویسنده
چکیده
Let A,B be two unital C∗−algebras. We prove that every almost unital almost linear mapping h : A −→ B which satisfies h(3uy + 3yu) = h(3u)h(y) + h(y)h(3u) for all u ∈ U(A), all y ∈ A, and all n = 0, 1, 2, ..., is a Jordan homomorphism. Also, for a unital C∗−algebra A of real rank zero, every almost unital almost linear continuous mapping h : A −→ B is a Jordan homomorphism when h(3uy + 3yu) = h(3u)h(y) + h(y)h(3u) holds for all u ∈ I1(Asa), all y ∈ A, and all n = 0, 1, 2, ... . Furthermore, we investigate the Hyers–Ulam–Rassias stability of Jordan ∗−homomorphisms between unital C∗−algebras by using the fixed points methods.
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