Operator Algebras before and after Jiang-Su Stability

本项目旨在研究无限维空间的转换方式。所涉及的各种变换统称为运算符。有一些行为良好的子集，这些算子最初是作为约翰·冯·诺依曼（John von Neumann）引入的工具而突出的，以进一步推动他在量子力学中的工作，现在被称为算子代数。首席研究员试图收集有关这些代数的详细信息。在算子代数类中，有一些可以通过简单地移动一个几何形状来获得，比如旋转一个圆。这些被称为与动力系统相关的代数。本项目将集中在这类代数上，旨在研究与拓扑动力系统相关的算子代数的严格比较的看似弱的技术条件是否包含看似强的Jiang-Su吸收条件。这将完成一个猜想的冬季和首席调查员代数的这种类型，一个猜想，已在很大程度上证实，否则。在没有Jiang-Su吸收的情况下，我们的目标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素的集合构成该代数的稠密子集。

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.