科研之友
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摘要
This article investigates a bijective map Phi between two von Neumann algebras, one of which has no central abelian projections, satisfying Phi([[A, B](*), C](*)) = [[Phi(A), Phi(B)](*), Phi(C)](*) for all A, B, C in the domain, where [A, B](*) = AB-BA* is the skew Lie product of A and B. We show that the map Phi(I)Phi is a sum of a linear *-isomorphism and a conjugate linear *-isomorphism, where Phi(I) is a self-adjoint central element in the range with Phi(I)(2) = I.
