论文标题
非线性地图保存了混合的Jordan Triple $η$ - $*$ - 因素之间的产品
Nonlinear maps preserving the mixed Jordan triple $η$-$*$-product between factors
论文作者
论文摘要
令$ \ MATHCAL {A} $和$ \ MATHCAL {B} $为两个因子Von Neumann代数，而$η$为非零的复数数字。已经证明了非线性射击$ ϕ：\ Mathcal A \ Mathcal a \ Mathcal b $满足$$ ϕ（[a，b] _ {*}^}^}^η\diamond_ηc）= [ac（a），ϕ（a），ϕ（b），ϕ（b）]答：$如果$η= 1，$，则$ ϕ $是线性$*$ - 同构，共轭线性$*$ - 同构，是线性$*$ - 同构的否定，或者是共轭线性$*$ - 同构的负数。如果$η\ neq 1 $且满足$ ϕ（i）= 1，则$ ϕ $是线性$*$ - 同构和偶联的线性$*$ - 同构。
Let $\mathcal{A}$ and $\mathcal{B}$ be two factor von Neumann algebras and $η$ be a non-zero complex number. A nonlinear bijective map $ϕ:\mathcal A\rightarrow\mathcal B$ has been demonstrated to satisfy $$ϕ([A,B]_{*}^η\diamond_η C)=[ϕ(A),ϕ(B)]_{*}^η\diamond_ηϕ(C)$$ for all $A,B,C\in\mathcal A.$ If $η=1,$ then $ϕ$ is a linear $*$-isomorphism, a conjugate linear $*$-isomorphism, the negative of a linear $*$-isomorphism, or the negative of a conjugate linear $*$-isomorphism. If $η\neq 1$ and satisfies $ϕ(I)=1,$ then $ϕ$ is either a linear $*$-isomorphism or a conjugate linear $*$-isomorphism.
