2013 Fiscal Year Final Research Report
Study on operator inequalities based on various analytic methods
| Project/Area Number |
23540215
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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 | Kyushu University |
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Principal Investigator |
KOSAKI Hideki 九州大学, 数理(科)学研究科(研究院), 教授 (20186612)
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| Co-Investigator(Kenkyū-buntansha) |
WATATANI Yasuo 九州大学, 数理学研究院, 教授 (00175077)
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| Co-Investigator(Renkei-kenkyūsha) |
HIAI Fumio 東北大学, 名誉教授 (30092571)
SANO Takashi 山形大学, 理学部, 教授 (20250912)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 作用素平均 / 正定値関数 / 量子情報理論 |
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| Research Abstract |
To get norm comparison results for operator means we have to check positive definiteness of ratios of relevant means. By computing Fourier transforms we have checked positive definiteness of a variety of ratios. We have also made use of the concept of infinite divisibility to establish this for some ratios whose explicit computations of Fourier transforms seem hopeless.
On the other hand, our technique was proved useful for study on completely positive maps appearing naturally in quantum information theory.
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