Mathematical Sciences: Local Index Invariants for Rings of Type I & II

数学科学：I 型环的局部索引不变量

• 批准号: 9103987
• 负责人: Richard Carey
• 金额: $ 5.04万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103987&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Local; Index; Invariants

Professor Carey will continue his work in operator theory concerning principal currents, local index, and Fredholm reciprocity in multivariable spectral theory. For operator rings of type II, this work involves relationships between determinant theory in operator algebras and plurisubharmonic functions. This project concerns Hilbert space operators which can be thought of as infinite matrices of complex numbers. Professor Carey's project will focus on a more geometric way of looking at these operators. The ultimate goal is to be able to classify and obtain a deeper understanding of large families of these objects, for they are important in almost all branches of pure and applied mathematics.

Carey教授将继续他在多变量谱理论中有关主电流、局部指数和Fredholm互易的算子理论方面的工作。对于II型算子环，本文研究了算子代数中的行列式理论与多次调和函数之间的关系。这个项目涉及希尔伯特空间算子，它可以被认为是无限的复数矩阵。凯里教授的项目将侧重于用更几何的方式来看待这些算子。最终目标是能够对这些对象的大家族进行分类并获得更深入的理解，因为它们在几乎所有纯数学和应用数学分支中都很重要。