Mathematical Sciences: Projects in Modern Analysis

数学科学：现代分析项目

• 批准号: 9102488
• 负责人: Paul Muhly
• 金额: $ 47.46万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102488&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Projects; Modern; Analysis

This award will support the research projects of a group of mathematicians whose work centers around operator theory and operator algebras. Some of the areas of investigation will be (i) multiplication operators on functional Hilbert spaces, (ii) polynomial hyponormality using multivariable techniques, (iii) construction of irreducible subfactors with index greater than four, (iv) invariant theory, Schur-Weyl duality, and tensor product structure of quantum groups at roots of unity, (v) dilation theory for algebras of operators and covariant systems, (vi) one-parameter deformations of generalized commutation relations, (vii) operator algebras generated by Toeplitz and singular integral operators with random symbol, and (viii) coordinatization techniques to analyze non-self-adjoint operator algebras. A central aspect of this research project is an investigation of Hilbert space operators. These objects can be thought of as infinite matrices of complex numbers but they often arise in a way more suited to various applications. In the research projects of these investigators a single operator is usually not the subject of study but rather large classes of operators called algebras. The structure of such algebras is one of the most intensively studied areas of mathematics.

该奖项将支持一群数学家的研究项目，其工作围绕运营商理论和操作员代数为中心。 Some of the areas of investigation will be (i) multiplication operators on functional Hilbert spaces, (ii) polynomial hyponormality using multivariable techniques, (iii) construction of irreducible subfactors with index greater than four, (iv) invariant theory, Schur-Weyl duality, and tensor product structure of quantum groups at roots of unity, (v) dilation theory for algebras of operators and协方差系统，（vi）通用换向关系的一参数变形，（vii）操作代数由Toeplitz和具有随机符号的单数积分算子产生的代数，以及（VIII）坐标技术，以分析非相互接合操作员。 该研究项目的一个主要方面是对希尔伯特太空运营商的调查。 这些对象可以被认为是复数的无限矩阵，但通常以更适合各种应用的方式出现。 在这些研究人员的研究项目中，单个操作员通常不是研究主题，而是大量的运营商称为代数。 这种代数的结构是数学最深入研究的领域之一。