Consider A as a unital \ (\) -algebra. Given elements A, B∈A, the operations A•B=AB+BA* and A, B*=AB−BA* represent the skew Jordan product and the skew Lie product, correspondingly. Within this study, we demonstrate that a nonlinear mapping Φ: A→A adhering to ΦA1•A2•…•An−1, An*=∑j=1nA1•A2•…•Aj−1•Φ (Aj) •Aj+1•…•An−1, An* for every A1, A2, …, An∈A with n≥3, then Φ is an additive \ (\) -derivation. As an application of our main results, we establish characterizations of prime \ (\) -algebras, standard operator algebras, von Neumann algebras without central summands of type I1, and factor von Neumann algebras.
Alam et al. (Mon,) studied this question.
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