@Article{JMS-57-2,
author = {Meilian, Gao and Zhao, Xingpeng},
title = {Nonlinear Mixed Lie Triple Derivations by Local Actions on Von Neumann Algebras},
journal = {Journal of Mathematical Study},
year = {2024},
volume = {57},
number = {2},
pages = {178--193},
abstract = {<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>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v57n2.24.04},
url = {https://global-sci.com/article/91131/nonlinear-mixed-lie-triple-derivations-by-local-actions-on-von-neumann-algebras}
}