Document Type
Article
Department/Program
Mathematics
Journal Title
Linear Algebra and Its Applications
Pub Date
2009
Volume
431
Issue
7-May
First Page
833
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.
Recommended Citation
Cui, Jianlian and Li, Chi-Kwong, Maps preserving product XY-YX* on factor von Neumann algebras (2009). Linear Algebra and Its Applications, 431(7-May), 833-842.
10.1016/j.laa.2009.03.036
DOI
10.1016/j.laa.2009.03.036
