2005 Fiscal Year Final Research Report Summary
Several constants of Banach spaces and its application
| Project/Area Number |
16540142
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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, Institute of Science of Technology, Professor, 自然科学系, 教授 (30018949)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Mikio Kyushu Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (50090551)
TAKAHASHI Yasuji Okayama Prefectural University, Faculty of Computer Science and System Engineering, Professor, 情報工学部, 教授 (30001853)
HATORI Osamu Niigata University, Institute of Science and Technology, Professor, 自然科学系, 教授 (70156363)
WATANABE Keiichi Niigata University, Institute of Science and Technology, Associate Professor, 自然科学系, 助教授 (50210894)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Banach space / direct sum / uniform convexity / smoothness / Clarkson inequality / Hanner inequality |
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| Research Abstract |
The geometry of Banach space is an important and useful object in the every branch of Mathematics and has many applications. In particular, the form of the unit ball is important. From this, many geometrical notions of Banach spaces are arised. In this research, we study various constants of Banach spaces, for example, von Neumann-Jordan constant, James constant and so on. In particular, we studied the followings results in this study.
(1) We considered Banach spaces defined by absolute norms and calculated the constants of special Banach spaces.
An application, we studied the geometrical structure of Banach spaces.
(2) We introduced the notion of ψ-direct sums of Banach spaces and we showed the necessary and sufficient conditions that the space is smooth and uniform smooth.
(3) We in part calculated the James constant of 2-dimensional Lorentz space.
(4) We characterized the uniform nonsquareness of ψ-direct sum of two Banach spaces.
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Research Products
(34 results)
