| Project/Area Number |
09640214
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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 | Okayama Prefectural University |
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Principal Investigator |
TAKAHASHI Yasuji Faculty of Computer Science and System and Engineering, Okayama Prefectural University, Professor, 情報工学部, 教授 (30001853)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAHASHI Sin-ei Yamagata University, Faculty of Technology, Professor, 工学部, 教授 (50007762)
SATO Ryotaro Okayama University, Faculty of Science, Professor, 理学部, 教授 (50077913)
KAWABATA Hiroaki Faculty of Computer Science and System Engineering, Okayama Prefectural Universi, 情報工学部, 教授 (70081271)
TAKAHASHI Hiromitsu Faculty of Computer Science and System Engineering, Okayama Prefectural Universi, 情報工学部, 教授 (30109889)
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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 | Banach space / Rademacher type, cotype / uniformly convex space / Clarkson inequality / Neumann-Jordan constant / normal structure / norm inequalities / vector valued random variables / タイプ・コタイプ / ノイマン・ジョルダン定数 / ラフカ不等式 / 超回帰性 / ルベ-グ・ボホナ-空間 / 確率測度 |
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| Research Abstract |
We considered some generalizations of classical norm inequalities in general Banach spaces from the operator theoretical and probability theoretical point of view, and using these inequalities we investigated functional-analytic, geometric and probabilistic properties of Banach spaces as well as the relations between these properties.
The main results obtained here are as follows.
1. Clarkson-type inequalities and geometry of Banach spaces :
(1) High-dimensional versions of the Clarkson inequality (CI) are given in the general Banach space setting from the probability theoretical point of view. In particular, a characterization of (CI) is given by the notions of Rademacher type and cotype.
(2) It is shown how Clarkson-type inequalities are inherited by the Lebesgue-Bochner spaces L_r (X) from a given Banach space X.
(3) Geometrical properties of Banach spaces are characterized using Clarkson-type inequalities.
2. Hanner, Hlawka and the other inequlities in Banach spaces : High-dimensional versions of hanner and Hlawka inequalities are given from the probability theoretical point of view, and geometric and probabilistic properties of spaces are described by these inequalities and the others.
3. Von Neumann-Jordan (NJ-) constant and geometry of Banach spaces : Some geometrical constants of Banach spaces X including NJ-constant C_<NJ>(X) and James constant J(X) are introduced, and geometrical properties of X are described in terms of these constants.
4. Applications to Banach space theory and other related areas : Some properties of functional analysis are investigated in connection with geometric and probabilistic properties. Some applications to vector valued ergodic theorems are also investigated.
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