| Project/Area Number |
09640203
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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 |
解析学
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| Research Institution | KYUSHU INSTITUTE OF TECHNOLOGY |
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Principal Investigator |
KATO Mikio KYUSHU INSTITUTE OF TECHNOLOGY,PROFESSOR, 工学部, 教授 (50090551)
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| Co-Investigator(Kenkyū-buntansha) |
HASHIMOTO Kazuo HIROSHIMA JOGAKUIN UNIVERSITY,PROFESSOR, 生活科学部, 教授 (00156275)
NAGAI Toshitaka KYUSHU INSTITUTE OF TECHNOLOGY,PROFESSOR, 工学部, 教授 (40112172)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1997: ¥1,700,000 (Direct Cost: ¥1,700,000)
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| Keywords | Von Neumann-Jordan constant / Clarkson-type inequality / Rademacher type, cotype / Banach space / Geometry of Banach spaces / normal structure / matrix operator / interpolation / Littlewood matrix / Lebesgue-Bochner space |
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| Research Abstract |
Geometrical properties of Banach spaces as well as related norm inequalities are investigated from an operator theoretical point of view. This approach allows a unifying treatment of them and also enables us to apply interpolation techniques in research of the Banach space geometry. Not only they have their own beauty and significance, but also they provide essential or useful notions and tools in various branches of analysis including applicable areas, which indicates the fundamental importance of this subject.
Major results are as follows.
1. On Clarkson-type inequalities :
(1) A sequence of Clarkson-type inequalities are characterized in the general Banach space setting by the notions of Rademacher type and cotype which are of great importance in "Probability in Banach Spaces".
(2) It is shown how Clarkson's and related inequalities are inherited by the Lebesgue-Bochner space L_r (X) from a given Banach space X, by which most of these inequalities known for various spaces are derived unifyingly.
2. On the von Neumann-Jordan (NJ-) constant of a Banach space a sort of modulus of skewness of the norm :
(1) A systematic way to calculate NJ-constant is given, by which all the previous results for various spaces and some new ones as well are obtained.
(2) A sequence of informations NJ-constant gives is presented, especially about type and cotype, uniform convexity, uniform non-squareness, super-reflexivity, normal structure and fixed point property, etc.
3. Several geometrical properties are charcterized unifyingly via behavior of operator norms of 1 matrices between finite dimensional X-valued l_p-spaces. In particular, a sequence of characterizations of uniformly non-square spaces is given, some of which are similar to the well-known one for uniform convexity.
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