Mathematical Sciences: Module Derivations of Banach Algebras
{'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}
The subject of this mathematical research project is                       the theory of Banach algebras, which may be thought of                          as linear algebra in infinitely many dimensions. One                            can do arithmetic (add and multiply) in this setting,                           and one can also take limits. A fundamental theme of                            research in this area is to understand how the arithmetic                       and the limit-taking influence one another. For instance,                       does a map between Banach algebras satisfying prescribed                        arithmetic identities automatically preserve limits?                            The principal investigators will work on questions of                           this nature.                                                                         More specifically, they will continue their investi-                       gation of the continuity  and algebraic structure of                            derivations from Banach algebras to modules. Necessary                          and sufficient conditions on the algebra and/or the                             module will be sought which will insure that each derivation                    is continuous, each continuous derivation into a dual                           bimodule is inner and each continuous derivation into                           the dual space of the algebra is inner. Particular                              atention will be paid to Banach algebras of integrable                          functions and other Banach algebras arising naturally                           in analysis and applications.
{'FirstName': 'Philip', 'LastName': 'Curtis', 'PI_MID_INIT': 'C', 'PI_SUFX_NAME': 'Jr.', 'PI_FULL_NAME': 'Philip C Curtis', 'EmailAddress': 'pcc@math.ucla.edu', 'NSF_ID': '000110061', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of California-Los Angeles', 'CityName': 'LOS ANGELES', 'ZipCode': '900244200', 'PhoneNumber': '3107940102', 'StreetAddress': '10889 WILSHIRE BLVD STE 700', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '36', 'CONGRESS_DISTRICT_ORG': 'CA36', 'ORG_UEI_NUM': 'RN64EPNH8JC6', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CALIFORNIA, LOS ANGELES', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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