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Changjing Li

Publications and source records attributed to Changjing Li.

2 recordsLinked to original sources
arXiv2022

Nonlinear mixed Jordan triple *-derivations on factors

Let $\mathcal{A}$ be a factor with dim$\mathcal{A}\geq2$. For $A, B\in\mathcal{A}$, define by $[A, B]_{*}=AB-BA^{\ast}$ and $A\bullet B=AB+BA^{\ast}$ the new products of $A$ and $B$. In this paper, it is proved that a map $Φ: \mathcal {A}\rightarrow \mathcal {A}$ satisfies $Φ([A, B]_{*}\bullet C)=[Φ(A), B]_{*}\bullet C+[A, Φ(B)]_{*}\bullet C+[A, B]_{*}\bullet Φ(C)$ for all $A, B,C\in\mathcal {A}$ if and only if $Φ$ is an additive $*-$derivation.

math.OA↗
arXiv2021

Nonlinear mixed Jordan triple *-derivations on *-algebras

Let $\mathcal {A}$ be a unital $\ast$-algebra. For $A, B\in\mathcal{A}$, define by $[A, B]_{*}=AB-BA^{\ast}$ and $A\bullet B=AB+BA^{\ast}$ the new products of $A$ and $B$. In this paper, under some mild conditions on $\mathcal {A}$, it is shown that a map $Φ:\mathcal {A}\rightarrow \mathcal {A}$ satisfies $Φ([A\bullet B, C]_{*})=[Φ(A)\bullet B, C]_{*}+[A\bullet Φ(B), C]_{*}+[A\bullet B, Φ(C)]_{*}$ for all $A, B,C\in\mathcal {A}$ if and only if $Φ$ 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.

math.OA↗