Linearity of (generalized) -Lie derivations and their structures on -algebras

IF 0.8 Q2 MATHEMATICS Advances in Operator Theory Pub Date : 2024-02-27 DOI:10.1007/s43036-024-00320-1

Behrooz Fadaee, Hoger Ghahramani, Wu Jing

引用次数: 0

Abstract

Let $ {\mathcal {A}} $ be a unital $*$-algebra with characteristic not 2 and containing a nontrivial projection. We show that each nonlinear $*$-Lie derivation on ${\mathcal {A}}$ is a linear $*$-derivation. Moreover, we characterize nonlinear left $*$-Lie centralizers and nonlinear generalized $*$-Lie derivations. These results are applied to standard operator algebras and von Neumann algebras in complex Hilbert spaces, which generalize some known results.

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$$*$$-Lie（广义）派生的线性及其在 $$*$$-gebras 上的结构

让 $ {\mathcal {A}} $是一个特征不为2的单空 $*$-代数，并且包含一个非线性投影。我们证明，${\mathcal {A}}$ 上的每个非线性 $*$-Lie 派生都是线性 $*$-derivation.此外，我们还描述了非线性左（*\)-Lie 中心子和非线性广义（*\)-Lie 衍生。这些结果被应用于复希尔伯特空间中的标准算子代数和冯-诺依曼代数，它们概括了一些已知结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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