Let \(M\subseteq B(X)\) be an algebra with nontrivial idempotents or nontrivial projections if M is a \(*\)-algebra and \({\mathcal {Z}}_{M}={\mathbb {C}}I\). In this paper, the notion of (strong) 2-local Lie automorphism normalized property is introduced and it is proved that if M has 2-local Lie automorphism normalized property and \(\Phi :M \rightarrow M\) is an almost additive surjective 2-local Lie isomorphism with idempotent decomposition property, then \(\Phi =\Psi +\tau \), where \(\Psi \) is an automorphism of M or the negative of an anti-automorphism of M and \(\tau \) is a homogenous map from M into \({\mathbb {C}}I\). Moreover, it is proved that nest algebras on a separable complex Hilbert space H with dim\(H>\)2 and factor von Neumann algebras on a separable complex Hilbert space H with dim\(H\ge 2\) have strong 2-local Lie automorphism normalized property.

令\(M\subseteq B(X)\)是一个具有非平凡幂等或非平凡投影的代数，如果M是一个\(*\) -代数和\({\mathcal {Z}}_{M}={\mathbb {C}}我\)。本文引入了（强）2-局部李自同构归一化性质的概念，证明了如果M具有2-局部李自同构归一化性质且\(\Phi :M \rightarrow M\)几乎是可加的满射2-局部烈同构与幂等分解性，然后\（\披= \帕普西+ \ tau蛋白\） ，其中\（\帕普西\）是一个同构中号或反构的负中号和\(\tau \)是从M到\({\mathbb {C}}I\)的同构映射。此外，证明了具有dim \(H>\) 2的可分离复Hilbert空间H上的嵌套代数和具有dim \(H\ge 2\)的可分离复Hilbert空间H上的因子冯诺依曼代数具有强2-局部李自同构归一化性质。