Year: 2024
Author: Meilian Gao, Xingpeng Zhao
Journal of Mathematical Study, Vol. 57 (2024), Iss. 2 : pp. 178–193
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v57n2.24.04
Journal of Mathematical Study, Vol. 57 (2024), Iss. 2 : pp. 178–193
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Nonlinear mixed Lie triple derivation ∗-derivation von Neumann algebra.