C ~*-代数状态空间上的Bures几何
Bures Geometry on C*-algebraic State Spaces
摘要：
本文详细讨论了单位元C*-代数的状态空间或部分状态空间上的Bures距离函数所引起的内部几何。作为一个关键的结果，局部膨胀函数的计算状态时，状态参数是一定要改变沿某些参数化曲线通过这个状态。参数化曲线被认为是那些拥有可微的本地实现为向量状态相对于一些unital *-表示在附近的状态的问题。对应于这类曲线的给定状态下的所有切线形式的空间被指定为具有二次范数的赋范线性空间，该二次范数以特征方式依赖于状态。在分析结构的局部膨胀函数特别强调的是放在描述这些部分的状态空间，在限制线元素将Finslerian型，并测地线凸子集。所有得到的结果都说明了例子，并得到的影响相比，已知的调查Uhlmann等人在有限维的情况下。
英文摘要：
The inner geometry induced by the Bures distance function on the state space of a unital C*-algebra, or on parts of it, is considered in detail. As a key result the local dilation function is calculated at a state when the state argument is bound to vary along certain parameterized curves passing through this state. The parameterized curves considered are those possessing differentiable local implementations as vector states relative to some unital *-representation in the vicinity of the state in question. The space of all tangent forms at a given state correspondent to this category of curves is specified as normed linear space with a quadratic norm which is depending from the state in a characteristic manner. In analyzing the structure of the local dilation function special emphasis is laid on describing such parts of the state space, in restriction to which the line element would be of Finslerian type, and which were geodesically convex subsets. All results obtained are illustrated by examples, and the implications obtained are compared to those known from the investigations of Uhlmann et al in the finite dimensional case.
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。
