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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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | commutative Banach algebra / Segal algebra / convolution measure algebra / quasi-topology / approximate identity / Hyers-Ulam stability / inequality / Banach algebra / BSE and BED / Fourier algebra / fixed point theorem / Ulam type stability / additive mapping / Chebyshev's inequality / Gelfand transform / Fourier algbera / Banach's fixed point theorem / Mazur-Ulam theorem / Jensen's inequality / Hyers-Ulam-Aoki-Rassias stability / functional equation / Volterra type integral equation / binary operation / complete metric space |
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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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Report
(4 results)
Research Products
(43 results)
