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.
{'FirstName': 'Vern', 'LastName': 'Paulsen', 'PI_MID_INIT': 'I', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Vern I Paulsen', 'EmailAddress': 'vern@math.uh.edu', 'NSF_ID': '000331153', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '126200', 'Text': 'MODERN ANALYSIS'}
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