Mathematical Sciences: RUI: Problems in Operator Theory and Matrix Analysis

数学科学：RUI：算子理论和矩阵分析中的问题

• 批准号: 9123841
• 负责人: Leiba Rodman
• 金额: $ 8.69万
• 依托单位: College of William and Mary
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-05-15 至 1995-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9123841&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Problems; Operator

Rodman intends to study a variety of interrelated problems in operator theory and matrix analysis. These include interpolation problems for matrix and operator valued functions, completions of matrices and operators, linear preservers, several aspects of perturbation theory, and spectrum assignment problems. Operator theory is that part of mathematics that studies the infinite dimensional generalizations of matrices. In particular, when restricted to finite dimensional subspaces, an operator has the usual linear properties, and thus can be represented by a matrix. The central problem in operator theory is to classify operators satisfying additional conditions given in terms of associated operators (e.g. the adjoint) or in terms of the underlying space. Operator theory underlies much of mathematics, and many of the applications of mathematics to other sciences.

罗德曼打算研究算子理论和矩阵分析中的各种相互关联的问题。 这些包括矩阵和算子值函数的插值问题、矩阵和算子的完成、线性保持器、微扰理论的几个方面以及频谱分配问题。 算子理论是研究矩阵无限维推广的数学部分。 特别是，当限制为有限维子空间时，算子具有通常的线性属性，因此可以用矩阵表示。 算子理论的中心问题是对满足根据关联算子（例如伴随）或基础空间给出的附加条件的算子进行分类。 算子理论是许多数学以及数学在其他科学中的许多应用的基础。