MASA与C* 代数的一类Ⅰ型闭面
MASA's and certain type I closed faces of C*-algebras
摘要：
Akemann、Anderson和Pedersen的一个结果表明，如果C* 代数A的纯态序列在某种意义上接近无穷大，则存在MASA B，使得每个态关于B具有唯一的扩张性质。我们推广这在两个方面：我们证明了B可以要求包含一个近似单位的A，我们表明，离散空间的基础上引用的结果可以被替换为一个全不连通的空间。我们考虑两种特殊类型的I型闭面，都与上述有关，原子闭面和封闭面与近封闭的极端边界。一个具体的问题是，一个原子的封闭面是否总是有一个“孤立点”。我们给出了一个反例，并证明了当原子面有近闭极端边界时，这个问题的答案是肯定的。我们证明了一个补充的Glimm定理的第一型C* 代数，其中产生于理论的第一型封闭面。我们的例子之一是I型闭面，它同构于每个非I型可分C* 代数的闭面，但不同构于任何I型C* 代数的闭面。
英文摘要：
A result of Akemann, Anderson, and Pedersen states that if a sequence of pure states of a C*-algebra A approaches infinity in a certain sense, then there is a MASA B such that each of the states has the unique extension property with respect to B. We generalize this in two ways: We prove that B can be required to contain an approximate identity of A, and we show that the discrete space which underlies the result cited can be replaced with a totally disconnected space. We consider two special kinds of type I closed faces, both related to the above, atomic closed faces and closed faces with nearly closed extreme boundary. One specific question is whether an atomic closed face always has an "isolated point". We give a counterexample for this and also show that the answer is yes if the the atomic face has nearly closed extreme boundary. We prove a complement to Glimm's theorem on type I C*-algebras which arises from the theory of type I closed faces. One of our examples is a type I closed face which is isomorphic to a closed face of every non-type I separable C*-algebra and which is not isomorphic to a closed face of any type I C*-algebra.
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。
