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2017 Fiscal Year Final Research Report

Study on operator means and related topics

Research Project

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Project/Area Number 26400120
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionKyushu 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

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Published: 2019-03-29  

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