论文标题
统一轨道的路径连接
Path-connected Closures of Unitary Orbits
论文作者
论文摘要
假设A和B是Unital c*-ergebras，A可分开。令REP（A，B）表示从A到B的所有Unital * - 肌形态的集合，并具有侧面收敛的拓扑结构。我们考虑何时关闭REP（a，b）中单个表示的统一轨道的问题。当A单独产生A时，第一作者给出了肯定的答案，而B是所有操作员在可分离的希尔伯特空间上的代数。我们将此结果扩展到所有可分离A。当A为AF或同质时，我们还给出了肯定的答案，而B是Von Neumann代数，或者A为Ash，B是有限的Von Neumann代数。
Suppose A and B are unital C*-algebras and A is separable. Let Rep(A,B) denote the set of all unital *-homomorphisms from A to B with the topology of pointwise convergence. We consider the problem of when the closure of the unitary orbit of a single representation in Rep(A,B) is path-connected. An affirmative answer was given by the first author when A is singly generated and B is the algebra of all operators on a separable Hilbert space. We extend this result for all separable A. We also give an affirmative answer when A is AF or homogeneous and B is a von Neumann algebra or when A is ASH and B is a finite von Neumann algebra.
