The Characterization of 2-Local Lie Automorphisms of Some Operator Algebras

Xiaochun Fang (), Xingpeng Zhao () and Bing Yang ()
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Xiaochun Fang: Tongji University
Xingpeng Zhao: Tongji University
Bing Yang: Tongji University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1959-1974

Abstract: 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.

Keywords: Normalized property; 2-local Lie automorphism; 47B49 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0507-4

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