Nonlinear Mixed Jordan Triple $ * $-Derivations on $ * $-Algebras
Changjing Li, D. Zhang
Abstract
Let $ {\mathcal{A}} $ be a unital $ \ast $ -algebra containing a nontrivial projection. Under some mild conditions on $ {\mathcal{A}} $ , it is shown that a map $ \Phi:{\mathcal{A}}\rightarrow{\mathcal{A}} $ is a nonlinear mixed Jordan triple $ * $ -derivation if and only if $ \Phi $ is an additive $ * $ -derivation. In particular, we apply the above result to prime $ \ast $ -algebras, von Neumann algebras with no central summands of type $ I_{1} $ , factor von Neumann algebras, and standard operator algebras.
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