论文标题
在Unital完全正面地图上的广义正交度量
Generalized Orthogonal Measures on the Space of Unital Completely Positive Maps
论文作者
论文摘要
EFFROS的经典结果将状态在C*-Algebra上的barycentric分解与状态的GNS表示相对于C*-Algebra的状态空间上的正交度量的分解。在本说明中，我们将这种方法采用在b（h）中值的c*代数上完全正面图的空间，连接了Unital完全正面映射的Barycentric分解，并使同一的最小STinespring膨胀的分离。这将EFFROS在非共同环境中的工作概括。我们通过引入一类特殊的Barycentric措施来做到这一点，我们称之为广义正交措施。我们通过提及一些广义正交度量的一些例子来结束这一说明。
A classical result by Effros connects the barycentric decomposition of a state on a C*-algebra to the disintegration of the GNS representation of the state with respect to an orthogonal measure on the state space of the C*-algebra. In this note, we take this approach to the space of unital completely positive maps on a C*-algebra with values in B(H), connecting the barycentric decomposition of the unital completely positive map and the dis-integration of the minimal Stinespring dilation of the same. This generalizes Effros' work in the non-commutative setting. We do this by introducing a special class of barycentric measures which we call generalized orthogonal measures. We end this note by mentioning some examples of generalized orthogonal measures.
