Operator Algebras before and after Jiang-Su Stability

这个项目的目的是研究无限维空间的转化方式。涉及的各种转换统称为运算符。这类算符的一些行为良好的子集最初是作为约翰·冯·诺伊曼为进一步研究量子力学而引入的工具而出现的，现在被称为算符代数。首席研究者试图收集关于这些代数的详细信息。在算子代数的类中，可以通过简单地移动几何形状来获得算子代数，例如旋转一个圆。这些被称为与动力系统相关的代数。本课题将集中在这类代数上，研究与拓扑动力系统相关的算子代数，在严格比较的看似较弱的技术条件下，是否存在看似较强的江-苏吸收条件的问题。这将完成温特和这类代数的主要研究者的一个猜想，这个猜想已经在很大程度上得到了其他方面的证实。在没有酱-苏吸收的情况下，我们的目的是证明这些代数至少具有一个不那么严格的性质，即这样一个代数的可逆元的集合构成了这个代数的稠密子集。

This project aims to study the way in which infinite-dimensional space can be transformed. The various transformations involved are collectively known as operators. There are some well-behaved subcollections of such operators that first came to prominence as a tool introduced by John von Neumann to further his work in quantum mechanics and that are now known as operator algebras. The principal investigator seeks to collect detailed information about these algebras. Within the class of operator algebras are those that can be obtained by simply moving a geometric shape around, such as rotating a circle. These are known as the algebras associated with dynamical systems. The project will concentrate on this class of algebras.The project aims to study the question of whether the seemingly weak technical condition of strict comparison entails the seemingly stronger condition of Jiang-Su absorption for the operator algebras associated with topological dynamical systems. This would complete a conjecture of Winter and the principal investigator for algebras of this type, a conjecture that has been largely confirmed otherwise. In the absence of Jiang-Su absorption the goal is to show that these algebras do at least possess a less stringent property, namely, that the set of invertible elements of such an algebra constitutes a dense subset of the algebra.