(untitled) (Contemporary Mathematics, 2024)
In this manuscript, we characterize the bijective mapping between two von Neumann algebras and with dim ⩾ 1. The mapping Λ is to satisfy the following condition on the mixed bi-skew Lie (Jordan) product , for all , where the bi-skew Lie (Jordan) product is defined as , and . Specifically, we elaborate on the properties of the mapping Λ, establishing that it is additive, a∗-somorphism, and linear.