论文标题
在$ \ ast $ -Algebras上保留三重产品的非线性地图
Nonlinear maps preserving sums of triple products on $\ast $-algebras
论文作者
论文摘要
令$ \ mathcal {a} $和$ \ Mathcal {b} $为两个Unital Complex $ \ ast $ -Algebras，以使$ \ Mathcal {a} $具有非平地投影。在本文中，我们研究了bi原始非线性映射$φ的结构：\ Mathcal {a} \ rightarrow \ Mathcal {b} $保留三产品$α_{1} abc+α__{1} abc+α_{2} a^{*} a^{*} a^{*} cb^} cab^{*}+α_{5} bca+α_{6} cb^{*} a^{*}，$，其中标量$ \ {α_{k} \} _ {k} _ {k = 1}^{6} $是满足某些条件的复杂数字。
Let $\mathcal{A}$ and $\mathcal{B}$ be two unital complex $\ast $-algebras such that $\mathcal{A}$ has a nontrivial projection. In this paper, we study the structure of bijective nonlinear maps $Φ:\mathcal{A}\rightarrow \mathcal{B}$ preserving sum of triple products $α_{1} abc+α_{2} a^{*}cb^{*}+α_{3} ba^{*}c +α_{4} cab^{*}+α_{5} bca+α_{6} cb^{*}a^{*},$ where the scalars $\{α_{k}\}_{k=1}^{6}$ are complex numbers satisfying some conditions.
