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Nonlinear $*$-Jordan triple derivations on von Neumann algebras

In: Mathematica Slovaca, vol. 68, no. 1
Fangfang Zhao - Changjing Li

Details:

Year, pages: 2018, 163 - 170
Keywords:
$*$-Jordan triple derivations, derivations, von Neumann algebras
About article:
Let $B(H)$ be the algebra of all bounded linear operators on a complex Hilbert space $H$ and $\mathcal{A}\subseteq B(H)$ be a von Neumann algebra with no central summands of type $I1$. For $A, B\in \mathcal{A}$, define by $A\bullet B=AB+BA*$ a new product of $A$ and $B$. In this article, it is proved that a map $Φ: \mathcal{A}\rightarrow B(H)$ satisfies $Φ(A\bullet B\bullet C)=Φ(A) \bullet B\bullet C+A\bullet Φ(B)\bullet C+A\bullet B\bulletΦ(C)$ for all $A, B,C\in\mathcal{A}$ if and only if $Φ$ is an additive $*$-derivation.
How to cite:
ISO 690:
Zhao, F., Li, C. 2018. Nonlinear $*$-Jordan triple derivations on von Neumann algebras. In Mathematica Slovaca, vol. 68, no.1, pp. 163-170. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0089

APA:
Zhao, F., Li, C. (2018). Nonlinear $*$-Jordan triple derivations on von Neumann algebras. Mathematica Slovaca, 68(1), 163-170. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0089
About edition:
Published: 23. 2. 2018