Mathematical Sciences: Operator Algebras and Reproducing Kernel Hilbert Spaces

9311487保尔森这个项目涉及三个主要研究方向。首先，发展了算子代数的Morita理论。这包括几个稳定的同构定理和对算子代数上投射模的更深入的研究。其次，该项目将研究算子空间几何和算子空间的张量积。第三，该项目将对解析再生核Hilbert空间进行研究。这项研究属于现代分析的一般领域，涉及算子或变换的空间结构。在任何数学领域中，一个基本问题是确定两个对象何时等价且它们的几何形状相似。在这项工作中，研究人员检查了空间上的变换族，并通过等价将这些变换或算子与结构范畴联系起来。关键是，已知的一种结构的理论通常可以被证明自然地适用于同等的结构。因此，方法是证明相当复杂的算子族具有自然等价*

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 ***