A study of geometric structure of Banach spaces and its applications
| Project/Area Number |
15K04920
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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 | Niigata University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
加藤 幹雄 信州大学, 工学部, 非常勤講師 (50090551)
三谷 健一 岡山県立大学, 情報工学部, 准教授 (00468969)
渡邉 恵一 新潟大学, 自然科学系, 教授 (50210894)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | バナッハ空間 / James定数 / Birkhoff直交 / Radon空間 / 幾何学定数 / von Neumann-Jordan定数 / absoluteノルム / π/2回転不変ノルム / Becknerの不等式 |
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| Outline of Final Research Achievements |
In the study of geometry of Banach spaces, two notions of orthogonality and geometric constant are important. First, we sucessed to characterize 2 dimensional Banach spaces with James constant √2. We published three papers (Math Nach, Mediter J Math, Math Inequal Appl) about this results. In the study of symmetry of Banach spaces, we studied the symmetric points of von Neumann algebras and so on. In particular, we characterized symmetric 2-dimmensional Banach spaces using generalized Day-James spaces.
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| Academic Significance and Societal Importance of the Research Achievements |
バナッハ空間における幾何学構造について、特に、2次元空間の構造がまだ解明されていなかったが、absoluteノルム空間の概念を用いて、その解明に成功した。それにより、抽象的だった、Radon空間がDay-James 空間を用いて、特徴付けしたことには、大きな意義がある。
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Report
(5 results)
Research Products
(85 results)
