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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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 関数解析 / von Neumann-Jordan定数 / James定数 / バナッハ空間のψ直和 / 不動点性 / uniform non [ell]^n 1-ness / Sharp mean inequality / modulus of smoothness / modulus of convexity / バナッハ空間のφ直和 / uniform non [ell]^n_1-ness / uniform non[ell]^n_l-ness |
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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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Report
(4 results)
Research Products
(124 results)
