von Neumann 代数上保持混合Jordan三重积的非线性映射

Nonlinear Maps Preserving Mixed Jordan Triple Products on von Neumann Algebras

中文关键词:  混合Jordan三重积  同构  von Neumann代数

英文关键词:mixed Jordan triple product  isomorphism  von Neumann algebras

中文摘要:

      本文证明了在没有中心交换投影的von Neumann代数上的一个双映射$\Phi$如果保持混合Jordan三重积, 则$\Phi(I)\Phi$是一个线性*-同构和一个共轭线性*-同构的和, 其中$\Phi(I)$是中心自伴元素且$\Phi(I)^{2}=I$. 同时给出了因子von Neumann 代数上保持混合Jordan三重积映射的结构.

英文摘要:

      In this paper, we prove that if a bijective map $\Phi$ preserves mixed Jordan triple products between von Neumann algebras with no central abelian projections, then $\Phi(I)\Phi$ is the sum of a linear $*$-isomorphism and a conjugate linear $*$-isomorphism, where $\Phi(I)$ is a self-adjoint central element in the range with $\Phi(I)^{2}=I$. Also, we give the structure of this map that preserves mixed Jordan triple products between factor von Neumann algebras.