2007 Fiscal Year Final Research Report Summary
RESEARCH ON GEOMETRIC STRUCTURES OF BANACH AND FUNCTION SPACES AND ψ-DIRECT SUMS
| Project/Area Number |
18540185
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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 (50090551)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAHASHI Yasuji OKAYAMA PREFECTURAL UNIVERSITY, FACULTY OF COMPUTER SCIENCE AND SYSTEM ENGINEERING, PROFESSOR (30001853)
SAITO Kichi-suke NIIGATA UNIVERSITY, FACULTY OF SCIENCE, PROFESSOR (30018949)
TAMURA Takayuki CHIBA UNIVERSITY, GRADUATE SCHOOL OF SOCIAL SCIENCES AND HUMANITIES, ASSISTANT PROFESSOR (30302582)
SUZUKI Tomonari KYUSHU INSTITUTE OF TECHNOLOGY, FACULTY OF ENGINEERING, ASSOCIATE PROFESSOR (00303173)
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| Project Period (FY) |
2006 – 2007
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| Keywords | ψ-direct sum of Banach spaces / fixed point property / normal structure / weak nearly uniform smoothness / uniform non-l^n_1-ness / von Neumann-Jordan type constant / sharp triangle inequality / Banach spaces |
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| Research Abstract |
Geometric structures of Banach and function spaces and also ψ-direct sums of Banach spaces are investigated. Major results are as follows.
(1)A sharp triangle inequality and its reverse inequality with n elements were obtained, where some conditions for equality attainedness were presented. We used them to investigate the uniform non-l^n_1-ness etc. of Banach spaces. We extended these inequalities and also we had some results on such type inequalities with a parameter.
(2)Since it was introduced by the author etc. in 2002, the-ψ-direct sums have been attracting a good deal of attention. In this research project we obtained a sequence of results on the-ψ-direct sums concerning weak nearly uniform smoothness, WORTH property, Schur property, and uniform non-l^n_1-ness etc. As extreme cases some interesting results on l_1 and l_∞-sums are included: In particular we constructed uniformly non-l^3_1 Banach spaces which are not uniformly non-square, but have the fixed point property for non-expansive mappings (resp. but are super-reflexive).
(3)We introduced the von Neumann-Jordan type and the James type constants and obtained several results on the uniform non-squareness and uniform normal structure etc. with these constants. Also we obtained some results on the weak modules of nearly uniform smoothness.
(4)In July, 2007 the head investigator participated in the International Workshop on Banach space, Operator Theory and Applications to Nonlinear Analysis held in Harbin, China and presented an invited talk and a special lecture for graduate students, where he introduced some recent results on the-ψ-direct sums of Banach spaces. We organized the Second International Symposium on Banach and Function Spaces 2006in September, 2006, Kitakyushu, Japan, and its proceedings Banach and Function Spaces II (pp.467)was published by Yokohama Publishers in 2008.
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[Presentation] バナッハ空間のψ直和について2007
Author(s)
加藤 幹雄, 高橋 泰嗣, 田村 高幸
Organizer
第16回関数空間セミナー
Place of Presentation
東京理科大学・森戸記念館
Year and Date
2007-12-26
Description
「研究成果報告書概要(和文)」より
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[Presentation] 三角不等式の精密化とその応用2007
Author(s)
斎藤 吉助, 三谷 健一, 加藤 幹雄, 田村 高幸
Organizer
京都大学数理解析研究所研究集会「バナッハ空間, 関数空間及び不等式の研究とその応用」
Place of Presentation
京都大学数理解析研究所
Year and Date
2007-06-07
Description
「研究成果報告書概要(和文)」より
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