Mathematical Sciences: Complex Banach Spaces
{'Code': '03040103', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
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Banach space theory is a basic tool of mathematical analysis            that has been of importance since its inception at the turn of                  the century.  In recent years, there has been a rebirth of                      interaction with other aspects of mathematical analysis -- such                 as harmonic analysis and operator theory -- and probability                     theory.  In particular, Banach space methods, in the hands of                   highly creative and powerful researchers, have led to fundamental               breakthroughs in these other fields, and in turn probabilistic                  methods have enriched the structure theory of Banach spaces                     themselves.  World centers of excellence in this area are in                    Israel, Paris, Warsaw, Ohio, and Texas.                                                 Professor Edgar's work reflects this broad point of view.               The thrust of his work has been to make available over the                      complex field, the vast array of analytic methods that exist in                 the theory of real Banach spaces.  His work is an interesting                   mixture of Banach space theory with complex analysis, probability               (martingales), and harmonic analysis.  In past work he has                      utilized pseudoconvex domains and plurisubharmonic functions to                 find analogs for complex Banach spaces of extreme points, vector                measures, martingale convergence, and Choquet-type theorems.                    Professor Edgar has put into place a foundation on which to build               a substantial theory.  This subject, in which Professor Edgar is                a leader, is in its infancy, and the current proposal will carry                forward its development.
{'FirstName': 'Gerald', 'LastName': 'Edgar', 'EmailAddress': None, 'StartDate': '01/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Ohio State University Research Foundation -DO NOT USE', 'CityName': 'Columbus', 'ZipCode': '432101016', 'PhoneNumber': '6146888734', 'StreetAddress': '1960 KENNY RD', 'CountryName': 'United States', 'StateName': 'Ohio', 'StateCode': 'OH'}
{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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