Mathematical Sciences: Joint K-spectral Sets and Subnormal Operators

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Operator theory is a central discipline in Modern Analysis. Its origins lie in the study of mathematical physics and partial equations in the early twentieth century. At that time, it was seen that numerous physical problems in the theory of equilibria, vibration, quantum theory, etc. could be studied productively via the integral equations that model the phenomena. In the ensuing years, the subject of operator theory has grown to a central position in such investigations, and in core mathematics as well. Also central to Modern Analysis is the related discipline of operator algebras in which one studies collections of operators simultaneously. As the mathematical construct which best transfers the concepts of probability, measure theory, topology, and geometry to noncommutative contexts, operator algebras relate to a rich and important array of applications, from within mathematics itself to physics and microbiology. The research of Professor Paulsen bridges both operator theory and operator algebras. A careful analysis of the internal structure theory of operator algebras and the maps between them is an increasingly important subject, and Professor Paulsen is an expert in such matters. In prior research, Professor Paulsen obtained important results concerning completely bounded maps between C*-algebras. His recent book on this subject is expected to open new areas of research for both single operator theorists as well as operator algebraists. In his current program, Professor Paulsen will study joint K-spectral sets, subnormal models, and Hilbert modules over function algebras. The former study should lead to insights into tensor products of nonself-adjoint operator algebras. The second area explores aspects of dilation theory, and the latter project relates to several topics in operator theory.