Abstract
Let \(\mathcal{A}\) be a prime \(\ast\)-algebra. In this paper, assuming that \(\Phi:\mathcal{A}\to\mathcal{A}\) satisfies \(\Phi(A\diamond B \diamond C)=\Phi(A)\diamond B \diamond C+A\diamond\Phi(B) \diamond C+A \diamond B \diamond \Phi(C)\) where \(A\diamond B = A^{*}B + B^{*}A\) for all \(A,B\in\mathcal{A}\), we prove that \(\Phi\) is additive an \(\ast\)-derivation.
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The research of the first author was supported by the Talented Young Scientist Program of the Ministry of Science and Technology of China (Iran-19-001).
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Darvish, V., Nouri, M. & Razeghi, M. Nonlinear Triple Product \(A^{*}B + B^{*}A\) for Derivations on \(\ast\)-Algebras. Math Notes 108, 179–187 (2020). https://doi.org/10.1134/S0001434620070196
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DOI: https://doi.org/10.1134/S0001434620070196