The study of operator monotone functions and its application to polynomials and operator perturbation
| Project/Area Number |
25400116
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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 | Ritsumeikan University (2014-2016)
Shimane University (2013) |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
KOSAKI HIDEKI 九州大学, 数理科学研究院, 教授 (20186612)
WATATANI YASUO 九州大学, 数理化学研究院, 教授 (00175077)
SETO MICHIO 島根大学, 総合理工学研究院, 准教授 (30398953)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | Operator functions / Operator monotone / Operator convex / Loewner's theorem / Pick functions / Gamma function / Operator inequality / Positive linear maps / Positive linear map / Kadison's inequality / Loewner-Heinz inequality / Orthogonal polynomials / Jacobi operator / 作用素単調関数 / Pick 関数 / 解析接続 / 作用素不等式 / Loewner の定理 |
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| Outline of Final Research Achievements |
It is known that an inner product of a unit vector and a vector function which is a transformation of the unit vector by the resolvent of a Jacobi operator is an operator monotone function. We had conversely proved that every operator monotone function is represented by using inner product.
We next gave a condition under which the converse of the Loewner-Heinz inequality holds using the perturbation of the identity operator. The paper on this result was published from Proceeding of the Edinburgh Math. Soc. Two relevant papers to this result were published as joint works. Further we have proved the Choi conjecture on positive linear maps on C*-algebras.
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Report
(5 results)
Research Products
(20 results)
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[Journal Article] Inverses of operator convex functions2016
Author(s)
Henrik L. Pedersen; Mitsuru Uchiyama
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Journal Title
Trend in Mathematics (Ordered Structures and Aplications: Positivity VII)
Volume: -
Pages: 363-370
DOI
ISBN
9783319278407, 9783319278421
Related Report
Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
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