Classifications of commutative Banach algebras and Banach modules and its applications
| Project/Area Number |
25400120
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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(Kenkyū-buntansha) |
TSUKADA Makoto 東邦大学, 理学部, 教授 (10120198)
KOBAYASHI Yuji 東邦大学, 理学部, 訪問教授 (70035343)
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| Co-Investigator(Renkei-kenkyūsha) |
HATORI Osamu 新潟大学, 自然科学系, 教授 (70156363)
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| Research Collaborator |
MIURA Takeshi 新潟大学, 自然科学系, 教授 (90333989)
TAKAGI Hiroyuki 信州大学, 理学部, 教授 (20206725)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | Banach algebra / Segal algebra / Fourier algebra / Lau algebra / quasi-topology / Hyers-Ulam stability / inequality / topological semigroup / BSE and BED / multipliers / fractional operation / inversion map / distributive law / Archimedean semigroup / fixed point theorem / Ulam type stability / linear isometry / Jensen type inequality / Archimedean group / differential equation / Jensen's inequality |
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| Outline of Final Research Achievements |
We have studied commutative Banach algebras successfully by introducing a
new notion of quasi-topology. It was started by the introduction of the class BSE by Takahasi and Hatori, and it guided us to dividing commutative Banach algebras into 4 classes. In cooperation with J. Inoue, we further have claried BSE and BED properties of abstract Segel algebras which extend the Segal algebras on locally compact abelian groups by Reiter to commutative Banach algebras and of new Segel algebras induced by local A-functions.
We applied these results to solutions of a decision problem related to multipliers of Lau algebras constructed by semisimple commutartive Banach algebras, of stability problems related to the Ulam-type stability, of certain inequalities on convex functions and of the structure of topological semigroups on the real numbers.
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Report
(4 results)
Research Products
(39 results)
