Study on operator means and related topics
Project/Area Number |
26400120
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Basic analysis
|
Research Institution | Kyushu University |
Principal Investigator |
KOSAKI Hideki 九州大学, 数理学研究院, 学術研究者 (20186612)
|
Co-Investigator(Kenkyū-buntansha) |
綿谷 安男 九州大学, 数理学研究院, 教授 (00175077)
|
Project Period (FY) |
2014-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | 作用素平均 / 作用素ノルム不等式 / 正定値関数 / 並列和 / 非有界作用素 / 絶対連続性 / ノルム不等式 / Heinz不等式 |
Outline of Final Research Achievements |
Some comparison results (in strong sense such as positive definiteness and/or infinite divisibility) for various means were proved. For instance monotonicity (in parameters) for binomial and more generally Stolarsky means was obtained. As a consequence many new norm inequalities for related operator means were established. Several notions of parallel sums for unbounded positive self-adjoint operators have been studied by some groups with certain additional domain conditions. A satisfactory theory free from any domain conditions was developed in our study. This theory seems to be a useful device for study of absolute continuity for general positive self-adjoint operators.
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Report
(5 results)
Research Products
(8 results)