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Opereator inequalities and their application to related fields

Research Project

Project/Area Number 23540200
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionOsaka Kyoiku University

Principal Investigator

FUJII Jun Ichi  大阪教育大学, 教育学部, 教授 (60135770)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords作用素不等式 / 情報理論 / 量子情報 / 基礎解析学 / 作用素平均 / 作用素エントロピー / 作用素幾何学 / 国際情報交換 / 国際情報交流 デンマーク / 国際情報交流 クロアチア
Research Abstract

10 papers for operator inequalities were published in this period. Among those, 2 papers are related to interpolation paths, and 2 to Jensen operator inequalities. Though results for geometrical considerations are not so many, almost all talks in the conferences are related to this.
In particular, my talk at the last March in Gakushuin University is on a discussion between interpolational means and the Karcher operator equations. My paper for this subject has already been accepted but not been published yet.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (38 results)

All 2014 2013 2012 2011 Other

All Journal Article (20 results) (of which Peer Reviewed: 10 results) Presentation (16 results) Book (1 results) Remarks (1 results)

  • [Journal Article] Ritsuo An operator inequality implying the usual and chaotic orders2014

    • Author(s)
      Fujii, Jun Ichi; Fujii, Masatoshi; Nakamoto
    • Journal Title

      Ann. Funct. Anal

      Volume: 5 Pages: 24-29

    • Related Report
      2013 Final Research Report
  • [Journal Article] An operator inequality implying the usual and chaotic orders2014

    • Author(s)
      Fujii, Jun Ichi; Fujii, Masatoshi; Nakamoto, Ritsuo
    • Journal Title

      Annals of Functional Analysis

      Volume: 5 Pages: 24-29

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Operator inequalities related to weak 2-positivity2013

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

      J. Math. Inequal

      Volume: 7 Pages: 175-182

    • Related Report
      2013 Final Research Report
  • [Journal Article] Bounds for an operator concave function2013

    • Author(s)
      Dragomir, Sever S.; Fujii, Jun Ichi; Seo, Yuki
    • Journal Title

      Electron. J. Linear Algebra

      Volume: 26 Pages: 192-200

    • Related Report
      2013 Final Research Report
  • [Journal Article] Operator inequalities related to weak 2-positivity2013

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

      Journal of Mathematical Inequalities

      Volume: 7 Pages: 175-182

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bounds for an operator concave function2013

    • Author(s)
      Dragomir, Sever S.; Fujii, Jun Ichi; Seo, Yuki
    • Journal Title

      The Electronic Journal of Linear Algebra

      Volume: 26 Pages: 192-200

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Interpolationality for symmetric operator means2012

    • Author(s)
      Fujii, Jun Ichi
    • Journal Title

      Sci. Math. Jpn

      Volume: 75 Pages: 267-274

    • NAID

      130007663384

    • Related Report
      2013 Final Research Report
  • [Journal Article] Upper estimations on integral operator means2012

    • Author(s)
      Fujii, Jun Ichi; Fujii, Masatoshi
    • Journal Title

      Sci. Math. Jpn

      Volume: 75 Pages: 217-222

    • NAID

      130007663392

    • Related Report
      2013 Final Research Report
  • [Journal Article] On 3-variable extension for the integer mean2012

    • Author(s)
      Fujii, Jun Ichi; Fujii, Masatoshi; Matsumoto, Akemi
    • Journal Title

      Sci. Math. Jpn

      Volume: 75 Pages: 85-94

    • NAID

      130007670137

    • Related Report
      2013 Final Research Report
  • [Journal Article] The Jensen inequality in an external formula2012

    • Author(s)
      Fujii, Jun Ichi; Pecaric, Josip; Seo, Yuki
    • Journal Title

      J. Math. Inequal

      Volume: 6 Pages: 473-480

    • Related Report
      2013 Final Research Report
  • [Journal Article] Cauchy-Schwarz inequality in semi-inner product C∗-modules via polar decomposition2012

    • Author(s)
      Fujii, Jun Ichi; Fujii, Masatoshi.; Moslehian, M. S.; Seo, Y
    • Journal Title

      J. Math. Anal. Appl

      Volume: 394

    • Related Report
      2013 Final Research Report
  • [Journal Article] Upper estimations on integral operator means2012

    • Author(s)
      Fujii, Jun Ichi; Fujii Masatoshi
    • Journal Title

      Sciantiae Mathematicae Japonicae

      Volume: 75

    • NAID

      130007663392

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Jensen inequality in an external formula2012

    • Author(s)
      Fujii, Jun Ichi; Pecaric, Josip; Seo, Yuki
    • Journal Title

      Journal of Mathematical Inequalities

      Volume: 6

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Cauchy-Schwarz inequality in semi-inner product C*-modules via polar decomposition2012

    • Author(s)
      Fujii, Jun Ichi.; Fujii, Masatoshi.; Moslehian, Mohanmad Sal.; Seo, Yuki
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 394

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Reverse Cauchy-Schwarz type inequalities in pre-inner product C ∗-modules2011

    • Author(s)
      Fujii, Jun Ichi; Fujii, Masatoshi; Moslehian, Mohammad Sal; Pečarić, Josip E.; Seo, Yuki
    • Journal Title

      Hokkaido Math. J

      Volume: 40, no. 3 Pages: 393-409

    • Related Report
      2013 Final Research Report
  • [Journal Article] An external version of the Jensen operator inequality2011

    • Author(s)
      Fujii, Jun Ichi
    • Journal Title

      Sci. Math. Jpn

      Volume: 73 Pages: 125-128

    • NAID

      10028221881

    • Related Report
      2013 Final Research Report
  • [Journal Article] Path of quasi-means as a geodesic2011

    • Author(s)
      Fujii Jun Ichi
    • Journal Title

      Linear Algebra and Its Application

      Volume: 434 Pages: 542-558

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] An external version of the Jensen operator inequality2011

    • Author(s)
      Fujii Jun Ichi
    • Journal Title

      Sciantiae Mathematicae Japonicae

      Volume: 73 Pages: 125-128

    • NAID

      10028221881

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Cauchy-Schwarz type inequalities in pre-inner product C*-modules2011

    • Author(s)
      Fujii Jun Ichi; Fujii Masatoshi; Moslehian Mohammad Sal; Pečarić Josip E; Seo Yuki
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 40 Pages: 393-409

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Operator Q-class functions2011

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

      Sciantiae Mathematicae Japonicae

      Volume: 73 Pages: 75-80

    • NAID

      10027790544

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] 補間的作用素平均の Karcher equation における再生性2014

    • Organizer
      日本数学会 2014年度春季年会
    • Place of Presentation
      学習院大学
    • Year and Date
      2014-03-18
    • Related Report
      2013 Final Research Report
  • [Presentation] 正定値行列の幾何構造について2013

    • Organizer
      RIMS 研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2013-11-07
    • Related Report
      2013 Final Research Report
  • [Presentation] 2 次正定値行列全体の hyperkahler 構造2013

    • Organizer
      日本数学会 2013年度秋季総合分科会
    • Place of Presentation
      愛媛大学
    • Year and Date
      2013-09-27
    • Related Report
      2013 Final Research Report
  • [Presentation] 作用素平均の補間的 path とその積分平均の評価2012

    • Organizer
      作用素論・作用素環論研究集会
    • Place of Presentation
      大阪教育大学
    • Year and Date
      2012-11-25
    • Related Report
      2013 Final Research Report
  • [Presentation] Integral means induced by interpolation paths of operator means2012

    • Organizer
      RIMS 研究集会
    • Year and Date
      2012-11-06
    • Related Report
      2013 Final Research Report
  • [Presentation] 作用素平均の補間的な path について2012

    • Organizer
      日本数学会 春季年会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-27
    • Related Report
      2013 Final Research Report
  • [Presentation] Integral means induced by interpolational paths2012

    • Author(s)
      藤井淳一
    • Organizer
      RIMS 研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Research-status Report
  • [Presentation] 作用素平均の補間的pathとその積分平均の評価2012

    • Author(s)
      藤井淳一
    • Organizer
      作用素論・作用素環研究会
    • Place of Presentation
      大阪教育大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 作用素平均の補間的なpath について2012

    • Author(s)
      藤井淳一
    • Organizer
      日本数学会 春季年会
    • Place of Presentation
      東京理科大学
    • Related Report
      2011 Research-status Report
  • [Presentation] External type of Jensen operator inequality2011

    • Organizer
      RIMS 研究集会スペクトル, 数域などの作用素の幾何的特性量を用いた作用素の構造研究
    • Year and Date
      2011-11-15
    • Related Report
      2013 Final Research Report
  • [Presentation] 作用素平均から派生した 3 整数平均2011

    • Organizer
      日本数学会 秋季分科会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-28
    • Related Report
      2013 Final Research Report
  • [Presentation] 作用素平均から派生した3整数平均2011

    • Author(s)
      藤井淳一、藤井正俊、松本明美
    • Organizer
      日本数学会 秋季年会
    • Place of Presentation
      信州大学
    • Related Report
      2011 Research-status Report
  • [Presentation] External type of Jensen operator inequality2011

    • Author(s)
      藤井淳一
    • Organizer
      RIMS研究集会「スペクトル、数域などの作用素の幾何的特性量を用いた作用素の構造研究 」
    • Place of Presentation
      京都大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 補間的作用素平均のKarcher equationにおける再生性

    • Author(s)
      藤井淳一
    • Organizer
      日本数学会 春季年会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] 正定値行列の幾何構造について

    • Author(s)
      藤井淳一
    • Organizer
      RIMS研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
  • [Presentation] 2次正定値行列全体のhyperkahler構造

    • Author(s)
      藤井淳一
    • Organizer
      日本数学会秋季分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Annual Research Report
  • [Book] Structural analysis of complex networks2011

    • Author(s)
      Matthias Dehmer et al
    • Total Pages
      486
    • Publisher
      Birkhauser/Springer
    • Related Report
      2011 Research-status Report
  • [Remarks]

    • URL

      http://www.osaka-kyoiku.ac.jp/~fujii/lhtml/index-j.html

    • Related Report
      2011 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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