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Maps preserving product XY-YX* on factor von Neumann algebras
Cui, Jianlian Li, Chi-Kwong
Cui, Jianlian
Li, Chi-Kwong
Abstract
Let A and B be two factor von Neumann algebras. For A, B is an element of A. define by [A, B](*) = AB - BA* the new product of A and B. In this paper, we prove that a nonlinear bijective map phi : A - > B satisfies phi([A, B](*)) = [phi(A), phi(B)](*) for all A, B is an element of A if and only phi is a *-ring isomorphism. In particular, if the von Neumann algebras A and B are type I factors, then phi is a unitary isomorphism or a conjugate unitary isomorphism. (C) 2009 Elsevier Inc. All rights reserved.
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2009-01-01
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Mathematics
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10.1016/j.laa.2009.03.036