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

Author

Listed:
  • Xiaochun Fang

    (Tongji University)

  • Xingpeng Zhao

    (Tongji University)

  • Bing Yang

    (Tongji University)

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.

Suggested Citation

  • Xiaochun Fang & Xingpeng Zhao & Bing Yang, 2020. "The Characterization of 2-Local Lie Automorphisms of Some Operator Algebras," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1959-1974, December.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:4:d:10.1007_s13226-020-0507-4
    DOI: 10.1007/s13226-020-0507-4
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