论文标题
希尔伯特太空张量产品的操作员同构
Operator Isomorphisms on Hilbert Space Tensor Products
论文作者
论文摘要
本文介绍了两个运算符代数$ L_1 $和$ L_2 $之间的同构，其中$ L_1 $是Hilbert-Schmidt操作员空间中的一组运算符，而L_2 $是张量产品空间上的一组运营商。接下来，我们将同构的同构与称为Choi的同构定理的众所周知的结果进行比较。 Choi同构的优势在于，它对积极的操作员进行了完全积极的地图。同构的优点之一是它适用于无限的尺寸希尔伯特空间，而Choi的同构仅适用于有限维度。另外，我们的同构保留了操作员产品，而Choi则没有。我们对同构的某些用途进行了简短的讨论。
This article presents an isomorphism between two operator algebras $L_1$ and $L_2$ where $L_1$ is the set of operators on a space of Hilbert-Schmidt operators and $L_2$ is the set of operators on a tensor product space. We next compare our isomorphism to a well-known result called Choi's isomorphism theorem. The advantage of Choi's isomorphism is that it takes completely positive maps to positive operators. One advantage of our isomorphism is that it applies to infinite dimensional Hilbert spaces, while Choi's isomorphism only holds for finite dimensions. Also, our isomorphism preserves operator products while Choi's does not. We close with a brief discussion on some uses of our isomorphism.
