Mathematical Sciences: Joint K-spectral Sets and Subnormal Operators

数学科学：联合 K 谱集和次正规算子

• 批准号: 8701498
• 负责人: Vern Paulsen
• 金额: $ 3.28万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701498&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Joint; spectral; Sets

Operator theory is a central discipline in Modern Analysis. Its origins lie in the study of mathematical physics and partial equations in the early twentieth century. At that time, it was seen that numerous physical problems in the theory of equilibria, vibration, quantum theory, etc. could be studied productively via the integral equations that model the phenomena. In the ensuing years, the subject of operator theory has grown to a central position in such investigations, and in core mathematics as well. Also central to Modern Analysis is the related discipline of operator algebras in which one studies collections of operators simultaneously. As the mathematical construct which best transfers the concepts of probability, measure theory, topology, and geometry to noncommutative contexts, operator algebras relate to a rich and important array of applications, from within mathematics itself to physics and microbiology. The research of Professor Paulsen bridges both operator theory and operator algebras. A careful analysis of the internal structure theory of operator algebras and the maps between them is an increasingly important subject, and Professor Paulsen is an expert in such matters. In prior research, Professor Paulsen obtained important results concerning completely bounded maps between C*-algebras. His recent book on this subject is expected to open new areas of research for both single operator theorists as well as operator algebraists. In his current program, Professor Paulsen will study joint K-spectral sets, subnormal models, and Hilbert modules over function algebras. The former study should lead to insights into tensor products of nonself-adjoint operator algebras. The second area explores aspects of dilation theory, and the latter project relates to several topics in operator theory.

算子理论是现代分析中的一个中心学科。 它的起源在于研究数学物理和部分 世纪早期的方程式。 当时是 看到了平衡理论中的许多物理问题， 振动，量子理论等可以通过 模拟这些现象的积分方程。 在随后的 多年来，算子理论的主题已经发展成为一个中心 在这样的调查中，以及在核心数学中的地位。 现代分析学的另一个中心是 研究算子集合的算子代数 同步 作为一种数学结构， 转移了概率、测度论、拓扑学 和几何到非对易上下文，操作符 代数涉及到一系列丰富而重要的应用， 从数学本身到物理学和微生物学。 Paulsen教授对桥梁两种算子的研究 理论与算子代数 仔细分析内部 算子代数的结构理论及其映射 是一个越来越重要的课题，保尔森教授是一个 这方面的专家。 在之前的研究中，保尔森教授 得到了关于完全有界映射的重要结果 C*-代数 他最近关于这个问题的书预计 为单算子理论家和 以及算子代数学家。 在他目前的计划中， 保尔森教授将研究联合K谱集， 次正规模型和函数代数上的希尔伯特模。 前一项研究应导致深入了解张量产品的 非自伴算子代数 第二个领域探索 膨胀理论的各个方面，后者涉及到 算子理论中的几个问题。