Mathematical Sciences: Research on Operators in Hilbert Space

数学科学：希尔伯特空间算子研究

• 批准号: 9200609
• 负责人: Lawrence Fialkow
• 金额: $ 4.62万
• 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: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9200609&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Operators; Hilbert

Fialkow will continue his study of several problems concerning systems of bounded linear operators on Hilbert space. These problems concern the following topics: joint hyponormality and related problems in the theory of moments; spectral theory of elementary operators; and majorization, factorization and invertible factor theorems in C*-algebras. One part of the research will concern structural models for subnormal, k- hyponormal, and weakly k-hyponormal operators, with an emphasis on unilateral weighted shifts; this study will also concern multidimensional power moment 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.

Fialkow将继续研究与Hilbert空间上的有界线性算子组有关的几个问题。这些问题涉及以下主题：矩理论中的联合亚正规性及相关问题；初等算子的谱理论；C*-代数中的优化、因式分解和可逆因子定理。研究的一部分将涉及次正规、k次正规和弱k次正规算子的结构模型，重点是单边加权移位；本研究还将涉及多维功率矩问题。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。