C* 代数上的极大酉混合态
Maximally unitarily mixed states on a C*-algebra
摘要：
研究了C* 代数的极大混合态集，推广了Alberti关于von Neumann代数的工作.我们证明了，不同于冯诺依曼代数，一个C* 代数的最大混合态的集合可能不弱 * 闭。然而，我们得到一个具体的描述弱 * 封闭的这一套，在tracial国家和国家的因素，通过简单的无痕的concurrentents。对于具有Dixandom性质或Hausdorff本原谱的C* 代数-代数，我们的研究得到了进一步的发展.在后一种情况下，我们得到一个具体的描述的最大混合状态的一组方面的痕迹和扩展的状态的一个封闭的双边理想。我们提出几个问题。
英文摘要：
We investigate the set of maximally mixed states of a C*-algebra, extending previous work by Alberti on von Neumann algebras. We show that, unlike for von Neumann algebras, the set of maximally mixed states of a C*-algebra may fail to be weak* closed. We obtain, however, a concrete description of the weak* closure of this set, in terms of tracial states and states which factor through simple traceless quotients. For C*-algebras with the Dixmier property or with Hausdorff primitive spectrum we are able to advance our investigations further. In the latter case we obtain a concrete description of the set of maximally mixed states in terms of traces and extensions of the states of a closed two-sided ideal. We pose several questions.
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