| Project/Area Number |
19340035
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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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 Kyushu University, 大学院・数理学研究院, 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)
植田 好道 九州大学, 大学院・数理学研究院, 准教授 (00314724)
増田 俊彦 九州大学, 大学院・数理学研究院, 准教授 (60314978)
内山 充 島根大学, 総合理工学部, 教授 (60112273)
日合 文雄 東北大学, 大学院・情報科学研究科, 教授 (30092571)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥13,000,000 (Direct Cost: ¥10,000,000、Indirect Cost: ¥3,000,000)
Fiscal Year 2010: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2009: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2008: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2007: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
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| Keywords | 作用素平均 / 正定値関数 / ノルム不等式 / ユニタリ不変ノルム / Jensen型不等式 / majorization理論 / 因子環 / 無限分割可能行列 / 作用素凹関数 |
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| Research Abstract |
Operator means can be constructed from certain scalar means in a natural fashion, and comparison of unitarily invariant norms of such operator means requires positive definiteness of ratios of corresponding scalar means. Positive definiteness for many such ratios was determined, and consequently many very precise norm inequalities (such as an abundance of generalizations of the Heinz inequality and monotonicity in a parameter of norms of operator binomial means) were obtained. Moreover, many such positive definite functions arising in this way were shown to be infinitely divisible. Also, Jensen-type majorization results and the equality condition for the trace Jensen inequality were proved in the setting of von Neumann algebras.
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