TY - JOUR
T1 - Nonlinear Mixed Lie Triple Derivations by Local Actions on Von Neumann Algebras
AU - Gao , Meilian
AU - Zhao , Xingpeng
JO - Journal of Mathematical Study
VL - 2
SP - 178
EP - 193
PY - 2024
DA - 2024/06
SN - 57
DO - http://doi.org/10.4208/jms.v57n2.24.04
UR - https://global-sci.org/intro/article_detail/jms/23168.html
KW - Nonlinear mixed Lie triple derivation, ∗-derivation, von Neumann algebra.
AB - <p style="text-align: justify;">As a generalization of global mappings, we study a class of non-global mappings in this note. Let $\mathcal{A} ⊆ B(\mathcal{H})$ be a von Neumann algebra without abelian direct
summands. We prove that if a map $δ:\mathcal{A}→\mathcal{A}$ satisfies $δ([[A,B]_∗,C]) = [[δ(A),B]_∗,C]+
[[A,δ(B)]_∗,C]+[[A,B]_∗,δ(C)]$ for any $A,B,C ∈ \mathcal{A}$ with $A^∗B^∗C =0,$ then $δ$ is an additive ∗-derivation. As applications, our results are applied to factor von Neumann algebras,
standard operator algebras, prime ∗-algebras and so on.</p>