Mathematical Sciences: Projects in Modern Analysis

这四名研究人员将研究与希尔伯特空间上的算子和算子的代数有关的各种问题。其中一个研究领域是多参数算子理论，在该理论中，像谱这样的概念是针对多个算子而不是单个算子以联合方式来考虑的。另一项研究涉及算子代数上的可微结构，包括对无界导子和李群作用的研究。我们将探索最近发现的纽结理论和算子代数理论之间的联系。希尔伯特空间的设置和变换它的线性运算符是表示数学中遇到的许多结构和现象的基础。这种设置的基本特征是无限维度，换句话说，无限多个自由度，以及不可交换性，换句话说，操作序列的结果取决于操作执行的顺序。本项目研究的总体目标是进一步扩展运营商表示事物的强大策略。

The four investigators will pursue a variety of problems having to do with operators and algebras of operators on Hilbert space. One area of research is multiparameter operator theory, in which such notions as spectrum are considered in joint fashion for tuples of operators rather than for single operators. Another line of investigation concerns differentiable structure on operator algebras, including the study of unbounded derivations and of Lie group actions. Recently discovered connections between knot theory and the theory of operator algebras will be explored. The setting of Hilbert space and the linear operators that transform it is fundamental for representing many of the structures and phenomena encountered in mathematics. Basic features of this setting are infinite-dimensionality, in other words infinitely many degrees of freedom, and noncommutativity, in other words the result of a sequence of operations depends on the order in which the operations are performed. The overall aim of the research in this project is to extend still further the powerful strategy of representing things by operators.