2005 Fiscal Year Final Research Report Summary
RESEARCH ON GEOMETRY OF BANACH AND FUNCTION SPACES AND INEQUALITIES
| Project/Area Number |
16540163
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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, FACULTY OF ENGINEERING, PROFESSOR, 工学部, 教授 (50090551)
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| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Tomonari KYUSHU INSTITUTE OF TECHNOLOGY, FACULTY OF ENGINEERING, ASSOCIATE PROFESSOR, 工学部, 助教授 (00303173)
TAKAHASHI Yasuji OKAYAMA PREFECTURAL UNIVERSITY, FACULTY OF COMPUTER SCIENCE AND SYSTEM ENGINEERING, PROFESSOR, 情報工学部, 教授 (30001853)
SAITO Kichi-suke NIIGATA UNIVERSITY, FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (30018949)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Hanner-type inequality / random Clarkson inequality / p-uniform smoothness / sharp triangle inequality / ψ-direct sum of Banach spaces / weak nearly uniform smoothness / B_n-convexity / fixed point property |
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| Research Abstract |
Geometric structures of Banach and function spaces were investigated especially in relation with some norm inequalities. Also ψ-direct sums of Banach spaces were investigated, which seem important as we can easily construct many examples of Banach spaces with a non l_p-type norm from a convex function ψ. Major results are as follows.
[1]On geometric structures of Banach and function spaces and norm inequalities :
(1)We extended the strong random Clarkson inequality, and characterized the Banach spaces in which the resulting inequality is valid are those of p-uniform smooth, or equivalently those of strong type p with the same constants involved them.
(2)We introduced Hanner-type inequalities with a weight and characterized 2-uniformly smooth, and 2-uniformly convex spaces with these inequalities. By changing the place of the weight, the resulting inequalities characterize p-uniformly smooth, and q-uniformly convex spaces. The best value of the weight in these inequalities were determined for L_p-spaces. A duality theorem for these Hanner-type inequalities was presented as well.
[2]We presented a sharp triangle inequality and its reverse in a Banach space.
[3]On ψ-direct sums of Banach spaces :
(1)We characterized the following properties of ψ-direct sums of Banach spaces :
smoothness, weak nearly uniform smoothness, WORTH property, Schur property etc. As an application we presented several examples of Banach spaces which are not uniformly non-square, but have the fixed point property.
(2)We characterized uniform non l^n_1-ness (B_n-convexity) particularly for the l_1-sum and l_∞-sum of Banach spaces.
[4]Some resuts were obatined on the James constant, on the relation between Property M and the fixed point property, and on the Banach-Mazur distance in relation with super-reflexivity etc.
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Research Products
(41 results)
