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

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

Journal of Mathematics, 2024, vol. 2024, 1-6

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.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1407653

DOI: 10.1155/2024/1407653

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