2015 Fiscal Year Final Research Report
Research on Jordan type model theory of weighted composition operators on Hilbert spaces
| Project/Area Number |
23540190
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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 | Niigata University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
IZUCHI Keiji 新潟大学, 自然科学系, フェロー (80120963)
SAITO Kichi-Suke 新潟大学, 自然科学系, フェロー (30018949)
HATORI Osamu 新潟大学, 自然科学系, 教授 (70156363)
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Keywords | operator inequality / operator theory / gyrogroup / gyrovector space |
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| Outline of Final Research Achievements |
It was the purpose of this project to construct a theory for continuous weighted composition operators on countably infinite dimensional Hilbert spaces corresponding to Jordan normal form of square matrices. While carrying out this project, we recognized relations with order preserving operator inequalities, nonassociative algebras and hyperbolic geometry. We gave some extensions of operator inequalities of Furuta type, and discovered and proved functional inequalities between certain kind of polynomials by applying matrix inequalities. Furthermore, we gave an elementary proof by hand calculation of that the balls in arbitrary real inner product spaces are not only gyrocommutative gyrogroup but also enjoying structure of gyrovector spaces, and it shows possibility of research by elementary approach of this subject.
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| Free Research Field |
関数解析学
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