Mathematical Sciences: Structures and Applications of       JB*Triples
{'Code': '03040103', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'William Y. Velez', 'PO_EMAI': None, 'PO_PHON': None}
This project is mathematical research on a class of objects,                known as Banach Jordan triple systems or JB*-triples, that are                  Banach spaces equipped with a compatible ternary product                        satisfying certain algebraic conditions.  Their study thus                      incorporates geometry in infinitely many dimensions, and a                      species of nonassociative algebra.  As the use of Jordan's name                 suggests, these structures have applications in mathematical                    physics and the foundations of quantum mechanics.  Strictly                     within mathematics, many useful consequences can be extracted                   once one knows that a given convex set is in fact the unit ball                 of a JB*-triple.                                                                    One specific objective of the research is to characterize                   geometrically the Banach spaces that are duals of JB*-triples.                  Derivations, bounded and unbounded, of JB*-triples will also be                 studied. Finally, the manifold consequences of changing the                     underlying field of scalars from the complex numbers to the real                numbers will be explored.
{'FirstName': 'Bernard', 'LastName': 'Russo', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Bernard Russo', 'EmailAddress': 'brusso@math.uci.edu', 'NSF_ID': '000447380', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of California-Irvine', 'CityName': 'IRVINE', 'ZipCode': '926970001', 'PhoneNumber': '9498247295', 'StreetAddress': '160 ALDRICH HALL', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '47', 'CONGRESS_DISTRICT_ORG': 'CA47', 'ORG_UEI_NUM': 'MJC5FCYQTPE6', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CALIFORNIA IRVINE', 'ORG_PRNT_UEI_NUM': 'MJC5FCYQTPE6'}
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{'Code': '126200', 'Text': 'MODERN ANALYSIS'}
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