Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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NONLINEAR ξ-LIE-⁎-DERIVATIONS ON VON NEUMANN ALGEBRAS

  • Yang, Aili (College of Science Xi'an University of Science and Technology)
  • Received : 2019.05.16
  • Accepted : 2019.11.13
  • Published : 2019.12.30
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Abstract

Let ℬ(ℋ) be the algebra of all bounded linear operators on a complex Hilbert space ℋ and 𝒨 ⊆ ℬ(ℋ) be a von Neumann algebra without central abelian projections. Let ξ be a non-zero scalar. In this paper, it is proved that a mapping φ : 𝒨 → ℬ(ℋ) satisfies φ([A, B]ξ⁎)= [φ(A), B]ξ⁎+[A, φ(B)]ξ⁎ for all A, B ∈ 𝒨 if and only if φ is an additive ⁎-derivation and φ(ξA) = ξφ(A) for all A ∈ 𝒨.

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Acknowledgement

Supported by : Shannxi Natural Science Foundation

The authors would like to thank the referee for excellent suggestions which helped us to improve considerably the first version of the article.

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