Mathematical Sciences: Operator Algebras and Reproducing Kernel Hilbert Spaces

小行星9311487 该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更深入的研究投射模算子代数。 第二，这个项目将研究算子空间几何和算子空间的张量积。 第三，该项目将进行分析再生核希尔伯特空间的研究。 这项研究是在一般领域的现代分析和关注的结构空间的运营商或变换。 任何数学领域的一个基本问题是确定两个物体何时等价且几何形状相似。 在这项工作中，研究人员研究了空间上的变换族，并通过等价关系将这些变换或运算符与结构类别联系起来。 关键在于，对于一种结构已知的理论，往往可以被证明自然地推广到一种等价的结构。 因此，方法是证明相当复杂的算子族具有自然等价性 *

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 ***