Research on geometric structures of Banach and function spaces with direct sums
| 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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Report
(5 results)
Research Products
(59 results)
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[Presentation] On A-direct sums of Banach spaces2016
Author(s)
Mikio Kato, Takayuki Tamura
Organizer
The fifth Asian conference on Nonlinear Analysis and Optimization
Place of Presentation
Toki Messe, Niigata, Japan
Year and Date
2016-08-01
Related Report
Int'l Joint Research / Invited
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[Presentation] On A-direct sums of Banach spaces2015
Author(s)
Takayuki Tamura, Sompong Dhompongsa, Mikio Kato
Organizer
The Fifth International Symposium on Banach and Function Spaces 2015
Place of Presentation
九州工業大学，北九州，日本
Year and Date
2015-09-02
Related Report
Int'l Joint Research / Invited
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