대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권4호
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  • Pages.1019-1028
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  • 2023
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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NONLINEAR MAPS PRESERVING THE MIXED PRODUCT *[X ⋄ Y, Z] ON *-ALGEBRAS

  • 투고 : 2023.02.01
  • 심사 : 2023.07.13
  • 발행 : 2023.10.31
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초록

Let 𝔄 and 𝔅 be unital prime *-algebras such that 𝔄 contains a nontrivial projection. In the present paper, we show that if a bijective map Θ : 𝔄 → 𝔅 satisfies Θ(*[X ⋄ Y, Z]) = *[Θ(X) ⋄ Θ(Y), Θ(Z)] for all X, Y, Z ∈ 𝔄, then Θ or -Θ is a *-ring isomorphism. As an application, we shall characterize such maps in factor von Neumann algebras.

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참고문헌

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