Nearly Jordan ∗‐Homomorphisms between Unital C∗‐Algebras

A. Ebadian, S. Kaboli Gharetapeh and M. Eshaghi Gordji

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

Abstract: Let A, B be two unital C∗‐algebras. We prove that every almost unital almost linear mapping h : A → B which satisfies h(3nuy + 3nyu) = h(3nu)h(y) + h(y)h(3nu) 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(3nuy + 3nyu) = h(3nu)h(y) + h(y)h(3nu) holds for all u ∈ I1 (Asa), all y ∈ A, and all n = 0,1, 2, …. Furthermore, we investigate the Hyers‐ Ulam‐Aoki‐Rassias stability of Jordan ∗‐homomorphisms between unital C∗‐algebras by using the fixed points methods.

Date: 2011
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https://doi.org/10.1155/2011/513128

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:513128

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