2012 Fiscal Year Final Research Report
Classifications of commutative Banach algebras and Banach modules and its applications
| Project/Area Number |
22540168
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Toho University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
HATORI Osamu 新潟大学, 大学院・自然科学系, 教授 (70156363)
TSUKADA Makoto 東邦大学, 理学部, 教授 (10120198)
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| Project Period (FY) |
2010 – 2012
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| Keywords | commutative Banach algebra / Segal algebra / convolution measure algebra / quasi-topology / approximate identity / Hyers-Ulam stability / inequality |
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| Research Abstract |
I n 1990, the author and the cooperation researchers, Prof. O. Hatori, introduced the class called BSE-algebras. In the present study, the author has successfully classified commutative Banach algebras by using the new concept that is called quasi-topology originating from BSE-algebras. Especially, with this classification, the author made clear the position of important commutative Banach algebras called Segal algebras. In addition, as applications of this classification, certain Ulam type stability problems are solved and several inequalities are derived for convex functions.
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