Mathematical Sciences: Projects in Modern Analysis

四名调查人员将追查各种问题 与希尔伯特上的算子和算子代数有关 空间 研究的一个领域是多参数算子理论， 其中以联合的方式考虑诸如频谱的概念 对于元组的操作符，而不是单个操作符。 另一个研究方向涉及可微结构 算子代数，包括无界算子代数的研究 导子和李群作用。 最近发现 纽结理论与算子理论的联系 代数将被探索。 希尔伯特空间的设置和线性算子， 转换它是表示许多 数学中遇到的结构和现象。 基本 这种设置的特征是无限维，在其他情况下， 无限多个自由度，以及不可交换性， 换句话说，一系列操作的结果取决于 执行操作的顺序。 总体目标 在这个项目中的研究是进一步扩展 一个强大的用操作符表示事物的策略。

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.