Nonlinear ∗-Jordan triple derivations on von Neumann algebras
-
Fangfang Zhao
and
Changjing Li
Abstract
Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H and 𝓐 ⊆ B(H) be a von Neumann algebra with no central summands of type I1. For A, B ∈ 𝓐, define by A ∙ B = AB+BA∗ a new product of A and B. In this article, it is proved that a map Φ: 𝓐 → B(H) satisfies Φ(A ∙ B ∙ C) = Φ(A) ∙ B ∙ C+A ∙ Φ(B) ∙ C+A ∙ B ∙Φ(C) for all A, B,C ∈ 𝓐 if and only if Φ is an additive *-derivation.
Acknowledgement
The authors would like to thank the referees for the very thorough reading of the paper and many helpful comments.
References
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