| Project/Area Number |
19540196
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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 | Okayama Prefectural University |
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Principal Investigator |
TAKAHASHI Yasuji Okayama Prefectural University, 情報工学部, 教授 (30001853)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAHASI Sin-ei 山形大学, 大学院・理工学研究科, 教授 (50007762)
KATO Mikio 九州工業大学, 大学院・工学研究院, 教授 (50090551)
曽布川 拓也 岡山大学, 教育学部, 准教授 (60252946)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | バナッハ空間の幾何学 / James定数 / von Neumann-Jordan定数 / 幾何学的定数 / 幾何学的性質 / ノルム不等式 / Geometry of Banach space / Uniform non-squareness / von Neumann-Jordan constant / James constant / Modulus of convexity / New geometric constant / Modulus of smoothness / Triangle inequality / Geometry of Banach spaces / Normal structure / Gao's constant / Hlawka inequality / Hlawka type inequality / James type constants / von Neumann-Jordan type constants / ψ-direct sums of Banach spaces |
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| Research Abstract |
We studied geometric constants and norm inequalities in Banach spaces. In particular the relation between James and von Neumann-Jordan constants was discussed intensively, and we obtained a quite simple inequality about these two constants. This answers affirmatively a question posed by Alonso-Martin-Papini, and improves all previous results concerning these inequalities. We also investigated refined generalizations of norm inequalities.
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