Mathematical Sciences: Operator Algebras and Their Applications

数学科学：算子代数及其应用

• 批准号: 8908281
• 负责人: Masamichi Takesaki
• 金额: $ 36.69万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8908281&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Operator; Algebras; Their

Professors Effros, Popa, and Takesaki will continue their investigations into operator algebra theory and its applications. Effros will focus on matricial norms and orderings. This is expected to lead to new approaches to Fourier analysis on non- abelian groups and to the structure theory of non-injective von Neumann algebras. Popa will work on the structure of factors, index theory for subfactors, amenability, and rigidity. Takesaki will study group actions on injective factors, and explore the relationship between modular theory for von Neumann algebras and Connes' cyclic cohomology. The Hilbert space operators that lie at the heart of this project may be thought of as a species of enriched numbers. They obey the same laws of arithmetic as numbers with two notable exceptions, namely that the result of multiplication depends on the order in which the factors are taken, and not every nonzero operator has an inverse. Mathematical analysis knows only two number systems, the real and complex, but there is an immense variety of operator algebras. Situations unsuitable for numerical representation can often be represented in some fashion by operator algebras, thanks to the greater degree of flexibility available with the latter. The price for this is that understanding the structure and classification of operator algebras requires considerable effort, as for instance the work to be undertaken in this project.

教授Effros，波帕，竹崎将继续他们的 研究算子代数理论及其应用。 Efros将专注于矩阵规范和排序。这是 预计将导致新的方法，傅立叶分析非- 阿贝尔群和非内射von Neumann代数波帕将致力于因素的结构， 子因素、顺从性和刚性的指数理论。竹崎 将研究群体行动的内射因素，并探讨 冯诺依曼代数的模理论与 Connes的循环上同调 希尔伯特空间算子是这个问题的核心， 项目可以被认为是一种丰富的数字。他们 和有两个显著数字的数字一样遵守算术定律 例外，即乘法的结果取决于 取因子的顺序，而不是每个非零 运算符有一个逆。数学分析只知道两个 数字系统，真实的和复杂的，但有一个巨大的 算子代数的变种不适合数字的情况 表示通常可以以某种方式表示为 算子代数，由于更大程度的灵活性 可与后者。代价就是 了解算子的结构和分类 代数需要相当大的努力，例如工作 在这个项目中进行。