Mathematical Sciences: Endomorphisms of von Neumann Algebras
{'Code': '03040103', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'William Y. Velez'}
This project involves mathematical research that is                        motivated by quantum mechanics. The quantum mechanical point of                 view is to represent observable quantities by linear operators on               Hilbert space rather than by scalars. In some models, the                       observables give rise to an algebra of operators. Time evolution                is given by a coherent rule specifying a transformation of the                  algebra at each moment. Mathematical manipulations allow one to                 read off properties of the system being modeled from the way it                 evolves over time. In the present undertaking, a rather general                 sort of time evolution, called a semigroup of endomorphisms, is                 to be studied with the goal of obtaining a scheme of                            classification.                                                                      More specifically, the problem of developing an index theory               for such semigroups in analogy with the index theory for                        unbounded hermitian operators will be investigated. A scheme for                classifying all adjoint-preserving semigroups of endomorphisms of               the algebra of bounded operators on Hilbert space for which there               is an intertwining semigroup of isometries will be sought.                      Results obtained for the latter situation will be applied to                    semigroups of endomorphisms of the hyperfinite factor.
{'FirstName': 'Robert', 'LastName': 'Powers', 'EmailAddress': None, 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Pennsylvania', 'CityName': 'Philadelphia', 'ZipCode': '191046205', 'PhoneNumber': '2158987293', 'StreetAddress': 'Research Services', 'CountryName': 'United States', 'StateName': 'Pennsylvania', 'StateCode': 'PA'}
{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8801162.xml'}