2016 Fiscal Year Final Research Report
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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| Keywords | Operator functions / Operator monotone / Operator convex / Loewner's theorem / Pick functions / Gamma function / Operator inequality |
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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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| Free Research Field |
関数解析・作用素論
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