Mathematical Sciences: RUI: Research on Operators in Hilbert Space

数学科学：RUI：希尔伯特空间算子研究

• 批准号: 9400566
• 负责人: Lawrence Fialkow
• 金额: $ 7.51万
• 依托单位: SUNY College at New Paltz
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400566&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Research; Operators

9400566 Fialkow The project involves work on several projects concerning operators on Hilbert spaces. These problems involve the following topics: joint hyponormality, especially k-hyponormality and weak k-hyponormality for weighted shifts; related problems in the theory of moments, including the complex truncated moment problem; majorization, factorization and invertible factor theorems in the theory of C*-algebras. One aspect of this research concerns structural and computational models for subnormal, k-hyponormal, and weakly k-hyponormal operators, with emphasis on unilateral shifts. This study also concerns multidimensional power moment problems, including the truncated complex moment problem and the extension problem for positive moment matrices. Another facet of this research concerns the description of the spectral picture of an elementary operator acting on a prime C*-algebra. This research also concerns solubility of the equation a = bx in a C*-algebra, including the case of solubility with x invertible. Operator theory is an infinite dimensional version of linear algebra and matrix theory. One of the important applications of linear algebra is in solving a system of a finite number of linear equations. The problem of solving operator equations can be considered as an attempt to solve a system involving a very large or infinite number of equations. Part of this project involves solving operator equations. Other portions of the project involves using operator theory to solve classical moment problems. The basic problem here is to determine a measure or mass distribution from various moments of mass. It is important to note that this research will be conducted at an undergraduate institution and will have significant impact in mathematics education. ***

小行星9400566 该项目涉及的工作在几个项目有关运营商的希尔伯特空间。这些问题涉及以下几个方面：联合亚正规性，特别是加权移位的k-亚正规性和弱k-亚正规性;矩理论中的相关问题，包括复截断矩问题; C*-代数理论中的优分解、因子分解和可逆因子定理。本研究的一个方面涉及次正规，k-亚正规，弱k-亚正规算子的结构和计算模型，重点是单边移位。本文还研究了多维幂矩问题，包括截断复矩问题和正矩矩阵的延拓问题。本研究的另一个方面涉及的描述的频谱图片的基本运营商作用于一个总理C*-代数。本文还研究了方程a = bx在C*-代数中的可解性，包括x可逆的可解性. 算子理论是线性代数和矩阵理论的无限维版本。线性代数的一个重要应用是求解有限个线性方程组。求解算子方程的问题可以被认为是试图解决一个涉及非常大或无限多个方程的系统。这个项目的一部分涉及求解算子方程。该项目的其他部分涉及使用算子理论来解决经典矩问题。这里的基本问题是从各种质量矩确定一个测度或质量分布。值得注意的是，这项研究将在本科院校进行，并将在数学教育产生重大影响。 ***