Abstract
It is shown that every almost ∗–homomorphism h : \({\fancyscript A}\) → ℬ of a unital JC*–algebra \({\fancyscript A}\) to a unital JC*–algebra ℬ is a ∗–homomorphism when h(rx) = rh(x) (r > 1) for all x ∈ \({\fancyscript A}\) , and that every almost linear mapping h : \({\fancyscript A}\) → ℬ is a ∗–homomorphism when h(2n u ∘y) = h(2n u) ∘ h(y), h(3n u ∘ y) = h(3n u) ∘ h(y) or h(q n u ∘ y) = h(q n u) ∘ h(y) for all unitaries u ∈ \({\fancyscript A}\) , all y ∈ \({\fancyscript A}\) , and n = 0, 1, . . . . Here the numbers 2, 3, q depend on the functional equations given in the almost linear mappings.
We prove that every almost ∗–homomorphism h : \({\fancyscript A}\) → ℬ of a unital Lie C*–algebra \({\fancyscript A}\) to a unital Lie C*–algebra ℬ is a ∗–homomorphism when h(rx) = rh(x) (r > 1) for all x ∈ \({\fancyscript A}\).
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The first author is supported by Grant No. R05–2003–000–10006–0 from the Basic Research Program of the Korea Science & Engineering Foundation.
The second author is supported by NNSF of China and NSF of Shanxi Province
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Park, C.G., Hou, J.C. & Oh, S.Q. Homomorphisms between JC*–algebras and Lie C*–algebras. Acta Math Sinica 21, 1391–1398 (2005). https://doi.org/10.1007/s10114-005-0629-y
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DOI: https://doi.org/10.1007/s10114-005-0629-y