Nonlinear Maps Preserving the Jordan Triple *-Product on Factor von Neumann Algebras

作者：Li, Changjing^*; Chen, Quanyuan; Wang, Ting

来源：Chinese Annals of Mathematics Series B, 2018, 39(4): 633-642.

DOI：10.1007/s11401-018-0086-4

• Jordan triple *-product
• Isomorphism
• von Neumann algebras

Let A and B be two factor von Neumann algebras. For A, B is an element of A, de fine by [A, B](*) = AB - BA* the skew Lie product of A and B. In this article, it is proved that a bijective map Phi : A -> B satisfies Phi([[A, B](*) , C](*)) = [[Phi(A), Phi(B)] (*), Phi(C)] (*) for all A, B, C is an element of A if and only if Phi is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.

• 出版日期2018-7
• 单位景德镇陶瓷大学; 南阳师范学院; 山东师范大学