Poisson <i>C</i>*-algebra derivations in Poisson <i>C</i>*-algebras

초록

In this study, we introduce the following additive functional equation: g(λu + v + 2y) = λg(u) + g(v) + 2g(y) for all λ ∈ C, all unitary elements u, v in a unital Poisson C*-algebra P, and all y ∈ P.Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of the aforementioned additive functional equation in unital Poisson C*-algebras.Furthermore, we apply to study Poisson C*-algebra homomorphisms and Poisson C*-algebra derivations in unital Poisson C*-algebras.

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