2010 Fiscal Year Final Research Report
The study of norm structure and various constants of Banach spaces, and its applications
| Project/Area Number |
20540158
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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 | Niigata University |
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Principal Investigator |
SAITO Kichi-Suke Niigata University, 自然科学系, 教授 (30018949)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Mikio 九州工業大学, 大学院・工学研究院, 教授 (50090551)
HATORI Osamu 新潟大学, 自然科学系, 教授 (70156363)
WATANABE Keiichi 新潟大学, 自然科学系, 准教授 (50210894)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKAHASHI Yasuji 岡山県立大学, 情報理工学部, 教授 (30001853)
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| Project Period (FY) |
2008 – 2010
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| Keywords | バナッハ空間 / James定数 / 三角不等式 |
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| Research Abstract |
To study norm structure of Banach spaces, it is important of considering the form of unit sphere of the space. Many mathematical results are dependent on the sphere. To do this, we have several geometrical constants of Banach spaces, for example, von Neumann-Jordan constant, James constant and so on. In this research, we calculate the geometrical constant of absolute normalized space R^2. In particular, we calculate the James constant of extreme absolute normalized norms on R^2.
On the other hand, we continued to study the refinement of sharp triangle inequalities. At first, we show another proof of sharp triangle inequality and we have the equality conditions of the inequalities. Further, we succeeded a generalization of the operator version of Dunkl-Williams inequality and so on.
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