Mathematical Sciences: Problems in Operator Theory and Nonselfadjoint Operator Algebras

数学科学：算子理论和非自共轭算子代数问题

• 批准号: 8802417
• 负责人: Hari Bercovici
• 金额: $ 4.39万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802417&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Operator; Theory

This project is for mathematical research in operator theory. The original impetus for this theory came from a fundamental insight in quantum mechanics, namely that physical quantities normally regarded as scalars are better represented by thinking of them as operators on Hilbert space, where they can interact in a more interesting fashion. The analysis of operators and how they transform the underlying space has since acquired a distinguished existence of its own, apart from physics. More specifically, Professor Bercovici will study a new class of nonselfadjoint operator algebras called dual algebras, with an emphasis on the existence and classification of invariant subspaces. He will enrich the perturbation theory of n-tuples of selfadjoint operators, and will also investigate skew Toeplitz operators. The latter study impinges significantly on control theory issues in engineering.

本课题是关于算子的数学研究 理论 这一理论的最初动力来自一个 量子力学中的基本观点，即物理 通常被认为是标量的量更好地表示为 把它们看作希尔伯特空间上的算子， 以更有趣的方式互动。 分析 运算符以及它们如何转换底层空间， 获得了自己的杰出存在，除了 物理学 更具体地说，贝尔科维奇教授将研究一种新的 一类非自伴算子代数称为对偶代数， 重点讨论了不变量的存在性和分类 子空间 他将丰富微扰理论的n元组， 自伴算子，也将调查斜Toeplitz 运营商 后一项研究对对照组影响很大 工程理论问题。