Nearly Jordan ∗-Homomorphisms between Unital C∗-Algebras

Abstract EN

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.