Abstract
Let , be two unital -algebras. We prove that every almost unital almost linear mapping : which satisfies for all , all , and all , is a Jordan homomorphism. Also, for a unital -algebra of real rank zero, every almost unital almost linear continuous mapping is a Jordan homomorphism when holds for all (), all , and all . Furthermore, we investigate the Hyers- Ulam-Aoki-Rassias stability of Jordan -homomorphisms between unital -algebras by using the fixed points methods.
Highlights
The stability of functional equations was first introduced by Ulam 1 in 1940
We prove that every almost unital almost linear mapping h : A → B is a Jordan homomorphism when h 3nuy 3nyu h 3nu hyhyh 3nu holds for all u ∈ U A, all y ∈ A, and all n 0, 1, 2, . . ., and that for a unital C∗-algebra A of real rank zero see 23, every almost unital almost linear continuous mapping h : A → B is a Jordan homomorphism when h 3nuy 3nyu h 3nu hyhyh 3nu holds for all u ∈ I1 Asa, all y ∈ A, and all n 0, 1, 2
We investigate the Hyers-Ulam-Aoki-Rassias stability of Jordan ∗-homomorphisms between unital C∗-algebras by using the fixed point methods
Summary
The stability of functional equations was first introduced by Ulam 1 in 1940 He proposed the following problem: given a group G1, a metric group G2, d and a positive number , does there exist a δ > 0 such that if a function f : G1 → G2 satisfies the inequality d f xy , f x f y < δ for all x, y ∈ G1, there exists a homomorphism T : G1 → G2 such that d f x , T x < for all x ∈ G1?. Rassias 4 for linear mappings by considering an unbounded Cauchy difference. This phenomenon of stability is called the Hyers-Ulam-AokiRassias stability
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