Mathematical Sciences: Operators on Hilbert Space

数学科学：希尔伯特空间上的算子

• 批准号: 9303776
• 负责人: Carl Pearcy
• 金额: $ 10.8万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303776&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Operators; Hilbert; Space

Pearcy will investigate the structure theory of various classes of operators that are related to contractions, including the polynomially bounded operators, power bounded operators, weakly centered operators, hyponormal operators, and pairs of commuting contractions. Techniques and results developed by Pearcy during the last 12 years involving the concept of dual algebra generated by one or several fixed bounded linear operators on Hilbert space will be used. 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.

皮尔西将研究与压缩有关的各种类型的算子的结构理论，包括多项式有界算子、幂有界算子、弱中心算子、次正规算子和交换压缩对。将使用由Hilbert空间上的一个或多个固定有界线性算子生成的对偶代数的概念，以及Pearcy在过去12年中开发的技术和结果。算子论是研究矩阵的无限维广义的数学部分。特别地，当被限制在有限维子空间时，算子具有通常的线性性质，因此可以用矩阵来表示。算子理论中的中心问题是根据伴随算子(例如伴随算子)或基础空间对满足附加条件的算子进行分类。算符理论是许多数学的基础，也是数学在其他科学中的许多应用。