关于标准式vN-algebras上的Bures距离
On Bures distance over standard form vN-algebras
摘要：
在标准式vN-代数的情况下，布勒斯距离是在正规正线性型上实现向量的纤维之间的自然距离。因此，众所周知，对于每两个正常的正线性型实现向量存在，使得通过所讨论的实现向量的度量距离获得Bures距离。我们讨论在何种程度上这可以保持真实的，如果一个纤维中的向量被认为是固定的。对于每一个非有限代数，类的反例给出和情况进行了分析，后者类型的结果必须失败。在本文的过程中，给出了这些事实和概念的说明，这些事实和概念可以被看作是有效地发展标准式vN-代数上的Bures几何的基础所需的基本C^*-代数工具的有用的最小值。
英文摘要：
In case of a standard form vN-algebra, the Bures distance is the natural distance between the fibres of implementing vectors at normal positive linear forms. Thereby, it is well-known that to each two normal positive linear forms implementing vectors exist such that the Bures distance is attained by the metric distance of the implementing vectors in question. We discuss to which extend this can remain true if a vector in one of the fibres is considered as fixed. For each nonfinite algebra, classes of counterexamples are given and situations are analyzed where the latter type of result must fail. In the course of the paper, an account of those facts and notions is given, which can be taken as a useful minimum of basic C^*-algebraic tools needed in order to efficiently develop the fundamentals of Bures geometry over standard form vN-algebras.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
