标题： $C^{*}$-子代数之间的距离以及一些规范关联的算子代数之间的关系 显示英文标题

标题： Relations amongst the distances between $C^{*}$-subalgebras and some canonically associated operator algebras

摘要： 我们证明了两个$C^*$-子代数$\mathcal{A}$和$\mathcal{B}$在一个$C^*$-代数$\mathcal{C}$中的 Christensen 距离（或 Kadison-Kastler 距离）等于它们的包络 von Neumann 代数$\mathcal{A}^{**}$和$\mathcal{B}^{**}$之间的距离（或张量积代数$\mathcal{A} \otimes^{\min} \mathcal{D}$和$\mathcal{B} \otimes^{\min} \mathcal{D}$之间的距离，对于任何单位交换$C^*$-代数$\mathcal{D}$）。 显示英文摘要

摘要： We prove that the Christensen distance (resp., the Kadison-Kastler distance) between two $C^*$-subalgebras $\mathcal{A}$ and $\mathcal{B}$ of a $C^*$-algebra $\mathcal{C}$ is equal to that between their enveloping von Neumann algebras $\mathcal{A}^{**}$ and $\mathcal{B}^{**}$ (resp., the tensor product algebras $\mathcal{A} \otimes^{\min} \mathcal{D}$ and $\mathcal{B} \otimes^{\min} \mathcal{D}$, for any unital commutative $C^*$-algebra $\mathcal{D}$).