Let M ⊑ B(X) be an algebra with nontrivial idempotents or nontrivial projections if M is a *-algebra and Z_M = ℂI. 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 Φ: M → M is an almost additive surjective 2-local Lie isomorphism with idempotent decomposition property, then → = Ψ + τ, where Ψ is an automorphism of M or the negative of an anti-automorphism of M and τ is a homogenous map from M into ℂI. Moreover, it is proved that nest algebras on a separable complex Hilbert space II with dimII >2 and factor von Neumann algebras on a separable complex Hilbert space H with dimH > 2 have strong 2-local Lie automorphism normalized property.

让中号⊑乙（X）是具有非平凡幂等或非平凡突起的代数如果中号是* -代数和Ž_中号=ℂ予。本文介绍了（强）2-局部Lie自同构归一化性质的概念，并证明了如果M具有2-局部Lie自同构归一化性质并且Φ：M→M是几乎加性的射影2-局部Lie同构与幂等分解性，然后→=Ψ+ τ，其中Ψ是的构中号或反构的负中号和τ是由同质地图中号ℂ我。此外，证明了在一个可分离复杂Hilbert空间套代数II昏暗II > 2和因子冯·诺依曼代数与dimH可分离复杂Hilbert空间H> 2有很强的2-局部烈构归一化属性。