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Developments and Applications for Operator Inequalities

Research Project

Project/Area Number 20540166
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOsaka Kyoiku University

Principal Investigator

FUJII Junichi  Osaka Kyoiku University, 教育学部, 教授 (60135770)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2010: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords関数解析 / 作用素不等式 / 作用素平均 / 量子情報理論 / 情報幾何
Research Abstract

The main results are on the Hiai-Petz geometry for positive definite matrices. Since I have been studying the Corach-Porta-Recht geometry for positive operators where the affine connection for the tangent bundle is essential, I can consider the Hiai-Petz one from this viewpoint. I have written 3 papers on this subject and made a special lecture at the spring meetings of the mathematical society of Japan. I have also written 5 papers on operator inequalities as the joint works with foreign or domestic fellows.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (21 results)

All 2011 2010 2009

All Journal Article (12 results) (of which Peer Reviewed: 12 results) Presentation (9 results)

  • [Journal Article] Mohammad Sal Moslehian, Operator Q-class functions2011

    • Author(s)
      Fujii Jun Ichi; Mohsen Kian;
    • Journal Title

      Sciantiae Mathematicae Japonicae 73

      Pages: 75-80

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Path of quasi-means as a geodesic2011

    • Author(s)
      Fujii Jun Ichi
    • Journal Title

      Linear Algebra and its Applications 434

      Pages: 542-558

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Path of quasi-means as a geodesic2011

    • Author(s)
      Fujii Jun Ichi
    • Journal Title

      Linear Algebra and its Applications

      Volume: 434 Pages: 542-558

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Operator Q-class functions2011

    • Author(s)
      Fujii Jun Ichi; Mohsen Kian; Mohammad Sal Moslehian
    • Journal Title

      Linear Algebra and its Applications

      Volume: 73 Pages: 75-80

    • NAID

      10027790544

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Hiai-Petz geodesic for strongly convex norm is the unique shortest path2010

    • Author(s)
      Fujii Jun Ichi
    • Journal Title

      Sciantiae Mathematicae Japonicae 71

      Pages: 19-26

    • NAID

      10027156113

    • Related Report
      2010 Final Research Report 2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Structure of Hiai-Petz parametrized geometry, for positive definite matrices2010

    • Author(s)
      Fujii Jun Ichi
    • Journal Title

      Linear Algebra and its Applications 432

      Pages: 318-326

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Structure of Hiai-Petz parametrized geometry2010

    • Author(s)
      Fujii Jun Ichi
    • Journal Title

      Linear Algebra and its Applications

      Volume: 432 Pages: 318-326

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Hiai-Petz geodesic for strongly convex norm is the unique shortestpath2010

    • Author(s)
      Fujii Jun Ichi
    • Journal Title

      Sciantiae Mathematicae Japonicae

      Volume: 71 Pages: 19-26

    • NAID

      10027156113

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Kantorovich type inequalities for the difference with two negative parameters2010

    • Author(s)
      Kim Young Ok; Fujii Jun Ichi; Fujii Masatoshi; Seo Yuki
    • Journal Title

      Sciantiae Mathematicae Japonicae

      Volume: 72 Pages: 171-183

    • NAID

      10026702810

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Structure of Hiai-Petz parametrized geometry for positive definite matrices2010

    • Author(s)
      Fujii Jun Ichi
    • Journal Title

      Linear Algebra and its Applications 432

      Pages: 318-326

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Kantorovich type inequality with a negative parameter2009

    • Author(s)
      Fujii Jun Ichi, Kim Young Ok
    • Journal Title

      Sciantiae Mathematicae Japonicae 69

      Pages: 87-92

    • NAID

      10025095126

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Kantorovich type inequality with a negative parameter2009

    • Author(s)
      Jun Ichi Fujii, Youg Ok Kim
    • Journal Title

      Sciantiae Mathematicae Japonicae 69

      Pages: 87-92

    • NAID

      10025095126

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] の外分点型作用素不等式について2011

    • Author(s)
      藤井淳一、Jensen
    • Organizer
      日本数学会春季総合分科会(アブストラクトにて発表相当と学会が公式承認)
    • Place of Presentation
      早稲田大学西早稲田キャンパス
    • Year and Date
      2011-03-22
    • Related Report
      2010 Final Research Report
  • [Presentation] Jensenの外分点型作用素不等式について2011

    • Author(s)
      藤井淳一
    • Organizer
      日本数学会春季総合分科会
    • Place of Presentation
      早稲田大学西早稲田キャンパス
    • Year and Date
      2011-03-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] 作用素平均族の評価式について2010

    • Author(s)
      藤井淳一
    • Organizer
      RIMS研究集会「作用素論における非可換構造の研究とその応用」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-29
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] べき作用素平均の差の評価式2010

    • Author(s)
      藤井淳一
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学東山キャンパス
    • Year and Date
      2010-09-23
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 正定値行列の幾何学と、測地線としてのquasi-means2010

    • Author(s)
      藤井淳一
    • Organizer
      日本数学会春季総合分科会
    • Place of Presentation
      慶応義塾大学矢上キャンパス
    • Year and Date
      2010-03-25
    • Related Report
      2010 Final Research Report
  • [Presentation] 正定値行列の幾何学と、測地線としての quasi-means2010

    • Author(s)
      藤井淳一
    • Organizer
      日本数学会 春季総合分科会
    • Place of Presentation
      慶応義塾大学 矢上キャンパス
    • Year and Date
      2010-03-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Hiai-Petzの幾何構造について2009

    • Author(s)
      藤井淳一
    • Organizer
      RIMS研究集会「作用素論における非可換解析学の展望」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-10-29
    • Related Report
      2010 Final Research Report
  • [Presentation] 正定値行列におけるHiai-Petz幾何のファイバー束について2009

    • Author(s)
      藤井淳一
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2009-09-26
    • Related Report
      2010 Final Research Report
  • [Presentation] 正定値行列における Hiai-Petz 幾何のファイバー束について2009

    • Author(s)
      藤井淳一
    • Organizer
      日本数学会 秋季総合分科会
    • Place of Presentation
      大阪大学 豊中キャンパス
    • Year and Date
      2009-09-26
    • Related Report
      2009 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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