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http://dx.doi.org/10.11568/kjm.2019.27.4.969

NONLINEAR ξ-LIE-⁎-DERIVATIONS ON VON NEUMANN ALGEBRAS  

Yang, Aili (College of Science Xi'an University of Science and Technology)
Publication Information
Korean Journal of Mathematics / v.27, no.4, 2019 , pp. 969-976 More about this Journal
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 ∈ 𝒨.
Keywords
${\ast}$-derivation; ${\xi}$-Lie-${\ast}$ derivations; von Neumann algebras;
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