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Analysis on geometric structures of operators in definite or indefinite inner product spaces

Research Project

Project/Area Number 20540152
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

SANO Takashi (SANO Takash)  山形大学, 理学部, 教授 (20250912)

Project Period (FY) 2008 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Keywords関数解析 / 作用素論 / 行列解析 / 行列 / 作用素 / レウナー行列 / クオン行列 / 作用素解析 / 一般化逆 / 条件付き負 / 作用素不等式 / 作用素環論 / 作用素単調 / 作用素凸 / 条件付正
Research Abstract

For selfadjoint operators/Hermitian matrices, we can define the order structure. For a real-valued function f we know the functional calculus by f. If this operation preserves the preceding order, then we say that f is operator/matrix monotone. It is well-known that this is equivalent to the positive-semidefiniteness of the corresponding Loewner matrices to f. Rajendra Bhatia and I studied the conditional positive/negative definiteness of Loewner matrices to have their characterization with applications. Fumio Hiai and I gave more precise arguments to have their generalizations.

Report

(7 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (49 results)

All 2014 2013 2012 2011 2010 2009 2008 Other

All Journal Article (17 results) (of which Peer Reviewed: 17 results) Presentation (28 results) (of which Invited: 3 results) Book (2 results) Remarks (2 results)

  • [Journal Article] Fr¥'echet derivatives for operator monotone functions2014

    • Author(s)
      T. Sano
    • Journal Title

      to appear in Linear Algebra and its Application

      Volume: 456 Pages: 88-92

    • DOI

      10.1016/j.laa.2013.05.018

    • URL

      http://www.sciencedirect.com/science/journal/00243795

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Loewner and Kwong matrices2012

    • Author(s)
      T. Sano, S. Tachibana
    • Journal Title

      Scientiae Mathematicae Japonicae

      Volume: 75 Pages: 335-338

    • NAID

      130007663505

    • URL

      http://www.jams.or.jp/notice/scmjol/

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Conditional negativity of anti-Loewner matrices2012

    • Author(s)
      C.Hidaka,T.Sano
    • Journal Title

      Linear and Multilinear Algebra

      Volume: 60 Issue: 11-12 Pages: 1265-1270

    • DOI

      10.1080/03081087.2011.627858

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Loewner matrices of matrix convex and monotone functions2012

    • Author(s)
      F. Hiai, T. Sano
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 64 Issue: 2 Pages: 343-364

    • DOI

      10.2969/jmsj/06420343

    • NAID

      10030740187

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Loewner and Kwong matrices2012

    • Author(s)
      T. Sano
    • Journal Title

      Sci. Math. Japonicae

      Volume: 75 Pages: 335-338

    • NAID

      130007663505

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Positivity and conditional positivity of Loewner matrices2010

    • Author(s)
      R. Bhatia, T.Sano
    • Journal Title

      Positivity

      Volume: 14 Issue: 3 Pages: 421-430

    • DOI

      10.1007/s11117-009-0027-2

    • Related Report
      2012 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical radius and unitarity2010

    • Author(s)
      T. Sano, A. Uchiyama
    • Journal Title

      Acta Sci. Math.(Szeged)

      Volume: 76 Pages: 581-584

    • URL

      http://acta.fyx.hu/acta/home.action?noDataSet=true

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Positivity and conditional positivity of Loewner matrices2010

    • Author(s)
      R.Bhatia, T.Sano
    • Journal Title

      Positivity 14

      Pages: 421-430

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Numerical radius and unitarity2010

    • Author(s)
      T.Sano, A.Uchiyama
    • Journal Title

      Acta Sci.Math.(Szeged) 76

      Pages: 581-584

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Numerical radius and unitarity2010

    • Author(s)
      T.Sano, A.Uchiyama
    • Journal Title

      Acta Sci.Math.(Szeged)

      Volume: 76 Pages: 581-584

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Loewner matrices and operator convexity2009

    • Author(s)
      R. Bhatia,T.Sano
    • Journal Title

      Math. Annalen

      Volume: 344 Issue: 3 Pages: 703-716

    • DOI

      10.1007/s00208-008-0323-3

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Young's inequality and trace2009

    • Author(s)
      K, Cho, T.Sano
    • Journal Title

      Linear Algebra and itsApplication

      Volume: 431 Issue: 8 Pages: 1218-1222

    • DOI

      10.1016/j.laa.2009.04.016

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Loewner matrices and operator convexity2009

    • Author(s)
      R.Bhatia, T.Sano
    • Journal Title

      Math.Annalen 344

      Pages: 703-716

    • Related Report
      2010 Self-evaluation Report 2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Young's inequality and trace2009

    • Author(s)
      K, Cho, T.Sano
    • Journal Title

      Linear Algebra and its Application 431

      Pages: 1218-1222

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Young's inequality and trace2009

    • Author(s)
      K.Cho, T.Sano
    • Journal Title

      Linear Algebra and its Application 431

      Pages: 1218-1222

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Loewner matrices and operator convexity2009

    • Author(s)
      R. Bhatia and T. Sano
    • Journal Title

      Math. Annalen 344

      Pages: 703-716

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical radius of Moore-Penrose inverse

    • Author(s)
      H. Ito, T. Sano, Y. Sato
    • Journal Title

      to appear in Scientiae MathematicaeJaponicae

    • NAID

      130007643025

    • URL

      http://www.jams.or.jp/notice/scmjol/

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Presentation] Loewner and Kwongmatrices2012

    • Author(s)
      佐野隆志
    • Organizer
      Matrices and Operators in honor ofsixtieth birthday of Rajendra Bhatia
    • Place of Presentation
      インド・バンガロール Iisc
    • Year and Date
      2012-12-30
    • Related Report
      2012 Final Research Report
  • [Presentation] Semi-operator monotonicity and derivatives for operator monotonefunctions2012

    • Author(s)
      佐野隆志
    • Organizer
      研究集会「幾何学及び確率論的手法による作用素の構造解析の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-11-06
    • Related Report
      2012 Final Research Report
  • [Presentation] Loewner and anti-Loewnermatrices2012

    • Author(s)
      佐野隆志
    • Organizer
      Positive Matrices and Operators: Recent Developments andAdvances
    • Place of Presentation
      韓国・テグ Kyungpook National University
    • Year and Date
      2012-06-26
    • Related Report
      2012 Final Research Report
  • [Presentation] Around Loewner matrices2012

    • Author(s)
      佐野隆志
    • Organizer
      日本数学会関数解析学特別講演
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-27
    • Related Report
      2012 Final Research Report
  • [Presentation] Around Loewner matrices2012

    • Author(s)
      T.Sano
    • Organizer
      日本数学会関数解析学特別講演
    • Place of Presentation
      東京理科大学(招待講演)
    • Year and Date
      2012-03-27
    • Related Report
      2011 Annual Research Report
  • [Presentation] Numerical radius andunitarity2011

    • Author(s)
      日高 知佳良、佐野隆志、Anti-Loewner matrices
    • Organizer
      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
      京都大学数理解析研究所
    • Year and Date
      2011-11-16
    • Related Report
      2012 Final Research Report
  • [Presentation] Anti-Loewner matrices ; Numerical radius and unitarity2011

    • Author(s)
      T.Sano, C.Hidaka
    • Organizer
      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
      数理解析研究所(招待講演)
    • Year and Date
      2011-11-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] Anti-Loewnermatricesについて2011

    • Author(s)
      日高 知佳良、佐野隆志
    • Organizer
      作用素論・作用素環論研究集会
    • Place of Presentation
      琉球大学
    • Year and Date
      2011-11-04
    • Related Report
      2012 Final Research Report
  • [Presentation] Anti-Loewner matricesについて2011

    • Author(s)
      T.Sano, C.Hidaka
    • Organizer
      作用素論・作用素環論研究集会
    • Place of Presentation
      琉球大学(招待講演)
    • Year and Date
      2011-11-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] Kwong行列について2011

    • Author(s)
      日高 知佳良、佐野隆志
    • Organizer
      研究集会「バナッハ空間論の研究とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-02-14
    • Related Report
      2012 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Loewner行列について2010

    • Author(s)
      佐野 隆志
    • Organizer
      作用素論・作用素環論研究集会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2010-11-13
    • Related Report
      2012 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Loewner行列について2010

    • Author(s)
      T.Sano
    • Organizer
      作用素論・作用素環論研究集会
    • Place of Presentation
      東京理科大学(招待講演)
    • Year and Date
      2010-11-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] 行列凸性や行列単調性とレウナー行列2010

    • Author(s)
      佐野 隆志
    • Organizer
      研究集会「作用素論における非可換構造とその応用」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-29
    • Related Report
      2012 Final Research Report 2010 Self-evaluation Report
  • [Presentation] 行列凸性や行列単調性とレウナー行列2010

    • Author(s)
      T.Sano
    • Organizer
      作用素論における非可換構造とその応用
    • Place of Presentation
      数理解析研究所(招待講演)
    • Year and Date
      2010-10-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] Loewner matrices and matrix convexity2010

    • Author(s)
      佐野隆志
    • Organizer
      16th Conference of theInternational Linear Algebra Society
    • Place of Presentation
      イタリア・ピサ
    • Year and Date
      2010-06-22
    • Related Report
      2012 Final Research Report
  • [Presentation] Loewner matrices and matrix convexity2010

    • Author(s)
      佐野隆志
    • Organizer
      16th Conference of the International Linear Algebra Society
    • Place of Presentation
      イタリア・ピサ
    • Year and Date
      2010-06-22
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Loewner matrices and matrix convexity2010

    • Author(s)
      T.Sano
    • Organizer
      16th Conference of the International Linear Algebra Society
    • Place of Presentation
      イタリアピサ(招待講演)
    • Year and Date
      2010-06-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] Operator monotone functions and Loewner matrices2009

    • Author(s)
      佐野隆志
    • Organizer
      ICTP Summer School and Advanced Workshop on Trendsand Developments in Linear Algebra
    • Place of Presentation
      イタリア・トリエステ
    • Year and Date
      2009-06-29
    • Related Report
      2012 Final Research Report
  • [Presentation] Operator monotone functions and Loewner matrices2009

    • Author(s)
      佐野隆志
    • Organizer
      ICTP Summer School and Advanced Workshop on Trends and Developments in Linear Algebra
    • Place of Presentation
      イタリア・トリエステ
    • Year and Date
      2009-06-29
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Operator monotone functions and Loewner matrices2009

    • Author(s)
      T.Sano
    • Organizer
      ICTP Summer School and Advanced Workshop on Trends and Developments in Linear Algebra
    • Place of Presentation
      ICTPトリエステ
    • Year and Date
      2009-06-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] Loewner行列について2009

    • Author(s)
      佐野 隆志
    • Organizer
      日本数学会東北支部会特別講演
    • Place of Presentation
      東北大学
    • Year and Date
      2009-02-21
    • Related Report
      2012 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Loewner行列について2009

    • Author(s)
      T. Sano
    • Organizer
      日本数学会東北支部会
    • Place of Presentation
      東北大
    • Year and Date
      2009-02-21
    • Related Report
      2008 Annual Research Report
  • [Presentation] Matrix inequalities andtrace2008

    • Author(s)
      佐野 隆志
    • Organizer
      インド・ラマニュジャン数学会
    • Place of Presentation
      インド・カンプール
    • Year and Date
      2008-05-21
    • Related Report
      2012 Final Research Report
  • [Presentation] Matrix inequalities and trace2008

    • Author(s)
      佐野隆志
    • Organizer
      インド・ラマニュジャン数学会
    • Place of Presentation
      インド・カンプール
    • Year and Date
      2008-05-21
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Matrix Inequalities and Trace2008

    • Author(s)
      T. Sano
    • Organizer
      インド・ラマヌジャン数学会
    • Place of Presentation
      インド工科大学カンプール校
    • Year and Date
      2008-05-21
    • Related Report
      2008 Annual Research Report
  • [Presentation] Loewner and anti-Loewner matrices

    • Author(s)
      T. Sano
    • Organizer
      Positive Matrices and Operators: Recent Developments and Advances
    • Place of Presentation
      Kyungpook National University, Korea.
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Semi-operator monotonicity and derivatives for operator monotone functions

    • Author(s)
      T. Sano
    • Organizer
      幾何学及び確率論的手法による作用素の構造解析の研究
    • Place of Presentation
      数理解析研究所
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Loewner and Kwong matrices

    • Author(s)
      T. Sano
    • Organizer
      Matrices and Operators in honor of sixtieth birthday of Rajendra Bhatia
    • Place of Presentation
      IIsc, Bangalore, India
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Book] マトリックスの世界2013

    • Author(s)
      佐野隆志
    • Publisher
      共立出版
    • Related Report
      2012 Final Research Report
  • [Book] マトリックスの世界2009

    • Author(s)
      佐野隆志
    • Publisher
      共立出版
    • Related Report
      2012 Final Research Report 2010 Self-evaluation Report 2009 Annual Research Report
  • [Remarks]

    • URL

      http://www-sci.yamagata-u.ac.jp/soumu/seeds/matSeedsFiles/sano.pdf

    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

      http://www-sci.kj.yamagata-u.ac.jp/English/GenInfo/Members/ResearchProfiles/Math/SANO.pdf

    • Related Report
      2012 Final Research Report

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Published: 2008-04-01   Modified: 2019-07-29  

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