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.

罗德曼打算研究操作者理论和矩阵分析中的各种相互关联的问题。 这些包括矩阵和操作员有价值功能的插值问题，矩阵和操作员的完成，线性保留器，扰动理论的几个方面以及频谱分配问题。 操作者理论是研究矩阵无限尺寸概括的数学部分。 特别是，如果仅限于有限的尺寸子空间，则操作员具有通常的线性属性，因此可以用矩阵表示。 操作者理论中的核心问题是对操作员进行分类，以满足相关操作员（例如伴随）或基础空间方面给出的其他条件。 操作者理论是数学的大部分基础，以及数学对其他科学的应用。