2010 Fiscal Year Final Research Report
Research on geometric structures of Banach and function spaces with applications
| Project/Area Number |
20540179
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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 | Kyushu Institute of Technology |
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Principal Investigator |
KATO Mikio Kyushu Institute of Technology, 大学院・工学研究院, 教授 (50090551)
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| Co-Investigator(Kenkyū-buntansha) |
SAITO KichiーSuke 新潟大学, 自然科学系, 教授 (30018949)
TAMURA Takayuki 千葉大学, 大学院・人文社会科学研究科, 助教 (30302582)
SUZUKI Tomonari 九州工業大学, 大学院・工学研究院, 准教授 (00303173)
TAKAHASHI Yasuji 岡山県立大学, 情報工学部, 名誉教授 (30001853)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 関数解析 |
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| Research Abstract |
We obtained a sequence of results on geometric structures of Banach spaces, especially for their ψ-direct sums. Major results are as follows. We showed a quite simple inequality between the von Neumann-Jordan and James constants, which refined all the previous results on their relation. We also showed another inequality which gives a unifying sight on these previous results. For ψ-direct sums, including the l_∞-sum, we characterized the uniform non-l^n1-ness, and weak nearly uniform smoothness (for finitely many Banach spaces). As applications some results on the fixed point property and super-reflexivity were given. Sharp mean triangle inequality was shown as well.
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[Journal Article] On the inequality C_<NJ>(X)≦J(X)2009
Author(s)
高橋泰嗣, 加藤幹雄
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Journal Title
In : "Banach and Function Spaces III", (Proceedings of the Third International Symposium on Banach and Function Spaces Kitakyushu, Japan Yokohama Publishers)(eds. M.Kato, L.Maligranda and T. Suzuki) in print.
Pages: 317-328
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