Mathematical Sciences: Operator Algebras and Reproducing Kernel Hilbert Spaces

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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 ***