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On Mixed Nonlinear Skew Lie (Jordan) Products on Von Neumann Algebras

Author

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  • Husain Alhazmi
  • Mohd Arif Raza
  • Abdul Nadim Khan
  • Tahani AL-Sobhi
  • Ali Jaballah

Abstract

Let U and V be von Neumann algebras. For D,E∈U, define by D,E∗=DE−ED∗D⋄E=DE+ED∗ the skew Lie (Jordan) product of D and E. In this manuscript, we study a bijective mapping Λ:U⟶V satisfying ΛD,E∗=ΛD⋄ΛE for all D,E∈U. Especially, we elaborate on the characteristics of the map Λ. The study revealed several constructive facts, leading to the conclusion that the map Λ is additive.

Suggested Citation

  • Husain Alhazmi & Mohd Arif Raza & Abdul Nadim Khan & Tahani AL-Sobhi & Ali Jaballah, 2024. "On Mixed Nonlinear Skew Lie (Jordan) Products on Von Neumann Algebras," Journal of Mathematics, Hindawi, vol. 2024, pages 1-6, June.
    • Handle: RePEc:hin:jjmath:1407653
    DOI: 10.1155/2024/1407653
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