Nonlinear mappings preserving Jordan multiple *- product on factor von Neumann algebras

作者：Huo, Donghua; Zheng, Baodong^*; Xu, Jinli; Liu, Hongyu

来源：Linear and Multilinear Algebra, 2015, 63(5): 1026-1036.

DOI：10.1080/03081087.2014.915321

• factor von Neumann algebras
• Jordan multiple product
• isomorphism

Let @@@ [GRAPHICS] @@@ and @@@ [GRAPHICS] @@@ be two factor von Neumann algebras. For @@@ [GRAPHICS] @@@ define by @@@ [GRAPHICS] @@@ the Jordan multiple @@@ [GRAPHICS] @@@ product in any fixed operation order. In this article, it is proved that a not necessarily linear bijective mapping @@@ [GRAPHICS] @@@ satisfies @@@ [GRAPHICS] @@@ if and only if @@@ [GRAPHICS] @@@ is a @@@ [GRAPHICS] @@@ ring isomorphism. In particular, if the von Neumann algebras @@@ [GRAPHICS] @@@ and @@@ [GRAPHICS] @@@ are type I factors, then @@@ [GRAPHICS] @@@ is a unitary isomorphism or a conjugate unitary isomorphism.

• 出版日期2015-5-4
• 单位哈尔滨工业大学; 牡丹江师范学院