Abstract
Let M ⊑ B(X) be an algebra with nontrivial idempotents or nontrivial projections if M is a *-algebra and ZM = 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.
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This work is partially supported by National Natural Science Foundation of China [Grant no. 11871375]
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Fang, X., Zhao, X. & Yang, B. The Characterization of 2-Local Lie Automorphisms of Some Operator Algebras. Indian J Pure Appl Math 51, 1959–1974 (2020). https://doi.org/10.1007/s13226-020-0507-4
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DOI: https://doi.org/10.1007/s13226-020-0507-4