Mathematical Sciences: Operator Algebras and Reproducing Kernel Hilbert Spaces

数学科学：算子代数和再现核希尔伯特空间

• 批准号: 9311487
• 负责人: Vern Paulsen
• 金额: $ 14.4万
• 依托单位: University of Houston
• 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: 1993-12-15 至 1997-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9311487&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Operator; Algebras; Reproducing

9311487 Paulsen This project concerns three main lines of research. First, developing a Morita theory for operator algebras. This includes several stable isomorphism theorems and a deeper study of projective modules over operator algebras. Second, the project will examine operator space geometry and tensor products of operator spaces. Third, the project will conduct a study of analytic reproducing kernel Hilbert spaces. This research is in the general area of modern analysis and concerns the structure of spaces of operators or transformations. A fundamental problem in any area of mathematics is determining when two objects are equivalent and their geometry is similar. In this work, the investigators examine the families of transformations on a space and relate these transformations or operators to categories of structures through equivalences. The point is that theory known for one structure can often be shown to carry naturally to an equivalent structure. Thus, the approach is to demonstrate that rather complex families of operators have natural equivalences ***

9311487 Paulsen这个项目涉及三个主要研究线。 首先，为操作员代数开发莫里塔理论。 这包括几种稳定的同构定理以及对操作员代数的投射模块的更深入研究。 其次，该项目将检查操作员空间的操作空间几何形状和张量产品。 第三，该项目将进行分析繁殖Hilbert空间的研究。 这项研究位于现代分析的一般领域，涉及操作员或转换空间的结构。 在任何数学领域的一个基本问题是确定两个对象何时等效，并且它们的几何形状相似。 在这项工作中，调查人员检查了空间上的转型家族，并通过等价将这些转换或操作员与结构类别联系起来。 关键是，一种结构已知的理论通常可以证明自然地携带到等效结构。 因此，方法是证明相当复杂的运营商具有自然等价的家族***