Research on geometric structures of Banach and function spaces with application of their [psi]-direct sums
| Project/Area Number |
23540216
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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, 教授 (50090551)
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| Co-Investigator(Kenkyū-buntansha) |
SAITO Kichi-suke 新潟大学, 自然科学系, 教授 (30018949)
TAMURA Takayuki 千葉大学, 人文社会科学研究科, 助教 (30302582)
SUZUKI Tomonari 九州工業大学, 工学研究院, 教授 (00303173)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | バナッハ空間のψ直和 / uniform non-squareness / WN uniform smoothness / von Neumann-Jordan定数 / absolute norm / 凸関数 / partial [ell]_1 norm / バナッハ空間の幾何学的定数 / partial [ell]_1-norm / バナッハ空間の幾何学 / 国際情報交換 / Banach space geometry / ψ-direct sum / convex function / geometric constant / James定数 / 弱uniform smooth性 / [ell]_1 type norm |
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| Research Abstract |
We characterized the weak nearly uniform smoothness of [psi]-direct sums of finitely many Banach spaces, where we introduced a class of convex functions which yield partial [ell]_1 norms on Cn. As an application, by constructing such a convex funtion we presented a plenty of Banach spaces with the fixed point property for nonexpansive mappings which are not uniformly non-square.
We introduced a geometric constant A(X) which is connected to the modulus of smoothness and obtained a sequence of results, and also concerning the von Neumann-Jordan constant of absolute norms on C2 we obtained a result which contains a couple of previous results.
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Report
(4 results)
Research Products
(79 results)
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[Journal Article] On the inequality C_{NJ}(X)<=J(X)2011
Author(s)
Y. Takahashi and M. Kato
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Journal Title
In : Banach and Function Spaces III, eds. M. Kato, L. Maligranda and T. Suzuki (Proc. The 3rd International Symposium on Banach and Function Spaces 2009)
Pages: 317-328
Related Report
Peer Reviewed
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