2007 Fiscal Year Final Research Report Summary
The form of unit balls and the constants of Banach spaces and their applications
| Project/Area Number |
18540164
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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 and Technology, Professor (30018949)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Mikio Kyushu Institute of Technology, Faculty of Engineering, Professor (50090551)
TAKAHASHI Yasuji Okayama Prefectural University, Faculty of Computer Science and System Engineering, Professor (30001853)
HATORI Osamu Niigata University, Institute of Science and Technology, Professor (70156363)
WATANABE Keiichi Niigata University, Institute of Science and Technology, Associate Professor (50210894)
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| Project Period (FY) |
2006 – 2007
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| Keywords | Banach space / uniform convexity / James constant / von Neumann-Jordan constant / triangle inequality / Lorentz space |
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| Research Abstract |
The form of unit balls of Banach spaces is an important and useful object in the every branch of Mathematics and has many applications. The study is deeply concerned with norm inequalities and the geometrical constant of Banach spaces.
At first, we showed the refinement of triangle inequality and the reverse inequality. As an application, we characterized the uniformly nonsquareness which is the important notion of the geometry of Banach spaces. The results were appeared in Math. Inequal. Appl. and J. Math. Anal. Appl.
Next we improved the theory of absolute normed spaces. Saito and Kato introduced the new notion of direct sums of Banach spaces. Using the direct sums of Banach spaces, Mitani and Saito presented the characterizations of important geometrical notions of Banach spaces, for example, uniform convexity, B-convexity, J-convexity and so on. The results appeared J. Math. Anal. Appl. and Banach J. Math.
Finally, the James constant of two dimensional Lorentz spaces was completely calculated by Mitani, Saito and Suzuki which was appeared in J. Math. Anal. Appl..
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