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: 9001090
• 负责人: Lawrence Fialkow
• 金额: $ 4.13万
• 依托单位: SUNY College at New Paltz
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001090&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Operators; Hilbert

Professor Fialkow will study several questions in multivariable operator theory concerning the structure of bounded linear operators in Hilbert space and the structure of certain associated C* algebras. One aspect of the research concerns the solution of systems of linear equations in C* algebras. Another facet involves polynomially bounded hyponormal weighted shifts. A final topic is the study of structural and spectral invariants for quasisimilarity of operators. The latter research is particularly concerned with characterizing those operators quasisimilar to the unilateral shift and determining their spectral properties. Hilbert space operators are essentially infinite matrices of complex numbers. These operators have applications in every area of applied science as well as in pure mathematics. This type of research is an attempt to classify certain important categories of such objects.

Fialkow教授将研究几个问题， 关于有界结构的多变量算子理论 Hilbert空间中的线性算子和某些 关联C* 代数 研究的一个方面涉及 C* 代数中线性方程组的解 另一 面涉及多项式有界亚正规加权移位。 最后一个主题是结构和谱不变量的研究 关于算子的拟相似性 后一项研究是 特别关注这些运营商的特征 类似于单边转移，并确定其 光谱特性 希尔伯特空间算子本质上是无穷矩阵， 复数 这些运营商在各个领域都有应用 在应用科学和纯数学中的应用。 这种类型的 研究是试图将某些重要类别分类 这样的物体。