Study on operator means and related topics

2017 Fiscal Year Final Research Report

• 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
• 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

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.

Free Research Field

数物系科学