2003 Fiscal Year Final Research Report Summary
The norm structure of Banach spaces and its application.
| Project/Area Number |
14540160
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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, Faculty of Science, Professor, 理学部, 教授 (30018949)
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| Co-Investigator(Kenkyū-buntansha) |
HATORI Osamu NIIGATA UNIVERSITY, Faculty of Science, Professor, 理学部, 教授 (70156363)
TAKAHASHI Yasuji Okayama Prefectural University, Faculty of Computer Science and System Engineering, Professor, 情報工学部, 教授 (30001853)
KATO Mikio Kyushu Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (50090551)
ASANO Kazuo NIIGATA UNIVERSITY, Faculty of Science, Lecturer, 理学部, 講師 (80000876)
SUZUKI Tomonari Kyushu Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (00303173)
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| Project Period (FY) |
2002 – 2003
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| Keywords | Banach space / uniform convex / strict convex / von Neumann-Jordan constant / James constant |
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| Research Abstract |
The study of Banach space theory is an important and useful object in the every branch of Mathematics and has many applications. In this Research, we study the rotundity and the nonsquareness of unit balls of Banach spaces. In particular, we attempt to study the absolute norms of C^n.
(1)At first, we defined the 4-direct sum of two Banach spaces and we showed the necessary and sufficient conditions that the space is strictly convex(resp.uniform convex).
(2)We proved the necessary and sufficient conditions that the absolute norm on C^n is smooth.
(3)We have the formulae of the James constant of absolute normed space on R^2 and we apply the Lorentz space.
(4)We study the uniform nonsquareness of C^n. We showed the uniform nonsquareness of 4-direct sum of two Banach spaces.
In the near future, we study the geometrical structure of the infinite dimensional Banach spaces, in particular, Schatten p-class operators c_p, Orliz space, noncommutativeL^p-space and so on.
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