| Project/Area Number |
26400131
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Shinshu University |
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Principal Investigator |
KATO Mikio 信州大学, 工学部, 非常勤講師 (50090551)
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| Co-Investigator(Kenkyū-buntansha) |
斎藤 吉助 新潟大学, 自然科学系, フェロー (30018949)
田村 高幸 千葉大学, 大学院社会科学研究院, 助教 (30302582)
鈴木 智成 九州工業大学, 大学院工学研究院, 教授 (00303173)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | バナッハ空間 / 直和 / 凸関数 / uniform non-square性 / uniform non-[ell]-n_1性 / 不動点性 / バナッハ空間の幾何学的定数 / James型定数 / Geometry of Banach space / direct sum / uniform non-squareness / convex function / fixed point property / geometric constant / James type constant / バナッハ空間の幾何学 / バナッハ空間の直和 / absolute norm / 幾何学的定数 / Banach space geometry |
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| Outline of Final Research Achievements |
A sequence of results on some geometric properties, especially, the uniform non-squareness, uniform non-[ell]-n_1-ness, and p-convexity, etc. were obtained for direct sums of Banach spaces. Especially, the problem to characterize uniform non-squareness for direct sums of "finitely many Banach spaces" was solved, which was the most important problem of this research program. As corollaries of the result on uniform non-[ell]-n_1-ness we obtained characterizations of this property for direct sums of Lp-spaces and for strictly monotone norms on CN (N: superscript). Several results on James-type constant J_t(X) of a Banach space X were also obtained. (Some of the above results are in preparation.)
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