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Additivity of maps preserving Jordan triple products on prime $$C^*$$C∗-algebras
Annals of Functional Analysis ( IF 1.2 ) Pub Date : 2020-01-01 , DOI: 10.1007/s43034-019-00009-0
Ali Taghavi , Ensiyeh Tavakoli

Let $$ \mathcal {A} $$ and $$\mathcal {B}$$ be two unital $$C^*$$-algebras such that $$ \mathcal {A} $$ contains a non-trivial projection $$P_1$$. In this paper, we investigate the additivity of maps $$ \varPhi $$ from $$\mathcal {A}$$ onto $$\mathcal {B}$$ that are bijective maps, that satisfy $$\begin{aligned} \varPhi \left( \frac{AB^*C+CB^*A}{2} \right) =\frac{\varPhi (A)\varPhi (B)^*\varPhi (C)+\varPhi (C)\varPhi (B)^*\varPhi (A)}{2} \end{aligned}$$for every $$ A, B, C\in \mathcal {A}$$. Moreover if $$ \mathcal {B} $$ is a prime $$C^*$$-algebra and $$ \varPhi (I)$$ is a positive element, then $$ \varPhi $$ is a $$*$$-isomorphism.

中文翻译:

在素数 $$C^*$$C∗-代数上保留 Jordan 三重积的地图的可加性

令 $$ \mathcal {A} $$ 和 $$\mathcal {B}$$ 是两个单位 $$C^*$$-代数,使得 $$ \mathcal {A} $$ 包含一个非平凡的投影 $ $P_1$$。在本文中,我们研究了从 $$\mathcal {A}$$ 到 $$\mathcal {B}$$ 的映射 $$ \varPhi $$ 的可加性,它们是双射映射,满足 $$\begin{aligned} \varPhi \left( \frac{AB^*C+CB^*A}{2} \right) =\frac{\varPhi (A)\varPhi (B)^*\varPhi (C)+\varPhi (C) )\varPhi (B)^*\varPhi (A)}{2} \end{aligned}$$对于每个 $$ A, B, C\in \mathcal {A}$$。此外,如果 $$ \mathcal {B} $$ 是素数 $$C^*$$-代数并且 $$ \varPhi (I)$$ 是一个正元素,那么 $$ \varPhi $$ 是一个 $$* $$-同构。
更新日期:2020-01-01
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