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Poisson C*-algebra derivations in Poisson C*-algebras

Wang Yongqiao, Park Choonkil, Chang Yuan

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20240053

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.