| Project/Area Number |
14F04320
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| Research Category |
Grant-in-Aid for JSPS Fellows
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| Allocation Type | Single-year Grants |
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| Section | 外国 |
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| Research Field |
Geometry
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| Research Institution | Kyoto University |
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Principal Investigator |
太田 慎一 京都大学, 理学研究科, 准教授 (00372558)
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| Co-Investigator(Kenkyū-buntansha) |
PALFIA MIKLOS 京都大学, 理学研究科, 外国人特別研究員
PALFIA Miklos 京都大学, 理学(系)研究科(研究院), 外国人特別研究員
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| Project Period (FY) |
2014-04-25 – 2016-03-31
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| Project Status |
Discontinued (Fiscal Year 2015)
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| Budget Amount *help |
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2015: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2014: ¥300,000 (Direct Cost: ¥300,000)
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| Keywords | 凸関数 / Loewner理論 / 多変数関数 / 作用素論 / リーマン幾何 / 曲率 / 勾配流 |
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| Outline of Annual Research Achievements |
In this academic year the researcher continued the work on extending Loewner’s theorem to several variables. The first result is an new LMI characterization of operator concave and monotone functions. This characterizes the functions as unique extremal solutions of linear matrix inequalities over some auxiliary Hilbert space. This result was presented at the ’Recent developments in operator algebras’ workshop in RIMS.
Later using this LMI representation an exact solution formula was established which seems to be the key to obtain the analytic continuation part of Loewner’s theorem. This part is still being carried out at the moment. As a by-product an infinite dimensional version of the theory of matrix convex sets and non-commutative Hahn-Banach theorems were established as key tools.
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| Research Progress Status |
27年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
27年度が最終年度であるため、記入しない。
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