Mathematical Sciences: Research on Operators in Hilbert     Space
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This project is mathematical research in operator theory, a                subject that had its origins in quantum mechanics (where                        operators on Hilbert space are used in place of scalars to                      represent physical quantities), but that has long since acquired                a vigorous life of its own.  Operators interact with one another                in a much richer way than do scalars, and individual operators                  carry a great deal of structure (spectrum, numerical invariants                 such as index, and so forth) whose elucidation is a perpetual                   challenge to the subject.                                                            Part of Professor Fialkow's research deals with spectrum and               index for so-called elementary operators, which are linear                      combinations of left and right multiplications.  The main thrust                here is to recover information about the given elementary                       operator in terms of multivariable spectral data from the pieces                of which it is composed.  Another aspect has to do with                         quasisimilarity, two operators being quasisimilar if they are                   intertwined left and right by a pair of injective transformations               with dense range;  the objective is to characterize the operators               that are quasimilar to the unilateral shift.
{'FirstName': 'Lawrence', 'LastName': 'Fialkow', 'PI_MID_INIT': 'A', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Lawrence A Fialkow', 'EmailAddress': 'fialkowl@newpaltz.edu', 'NSF_ID': '000158011', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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