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Operator space and Its application

Research Project

Project/Area Number 22540220
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionChiba University

Principal Investigator

NAGISA Masaru  千葉大学, 理学(系)研究科(研究院), 教授 (50189172)

Co-Investigator(Renkei-kenkyūsha) 伊藤 隆  群馬大学, 教育学部, 教授 (40193495)
松井 宏樹  千葉大学, 大学院理学研究科, 教授 (40345012)
Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords作用素単調関数 / Pick関数 / 作用素空間 / Haagerupテンソル積 / Schur積 / 作用素の正値性 / 作用素環 / 完全正写像 / シュアー積 / 作用素論 / Petz-Hasegawa の関数 / Haagerup テンソル積 / 極大可換部分環 / 完全正値 / 完全有界 / ペッツ長谷川の関数 / 量子状態空間 / 単調距離 / 数域半径 / 単元生成 / 完全有界写像
Research Abstract

It is well-known that the theory of matrices is a useful tool for the field of Applied Mathematics. We use the terminology "Operators" as Matrices in infinitely dimensional spaces. In the theory of operators, many unexpected phoenomena occur and such phoenomena do not occur in finitedimensional spaces. In the theory of Operator Algebra or Operators, such phoenomena sometimes occur in the argument in the convergence or not with respect to some norms. We study such facts using the notion of positivity. Operator monotone functions means functions which preserve the order of operators under functional cauculus and monotonicity for matrices is equivalent to that for Operators. We can get the characterization of operator monotonicity for many functions. We also get the characterization of extended Haagerup tensor product for Operator spaces. Using the Schur product of operators, we could realize the result for operator spaces.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (29 results)

All 2014 2013 2012 Other

All Journal Article (10 results) (of which Peer Reviewed: 7 results) Presentation (17 results) (of which Invited: 4 results) Remarks (2 results)

  • [Journal Article] On the extended Haagerup tensor product in Operator spaces2014

    • Author(s)
      伊藤隆, 渚勝
    • Journal Title

      J. of Korean Math. Soc.

      Volume: 51 Pages: 345-362

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the extended Haagerup tensor product in Operator spaces2014

    • Author(s)
      Takashi Ito, Masaru Nagisa
    • Journal Title

      Journal of the Korean Mathematical Society

      Volume: 51

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Order of operators determined by operator mean2014

    • Author(s)
      Masaru Nagisa, Mitsuru Uchiyama
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 印刷中

    • NAID

      130007961972

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some operator monotone functions related to Petz-Hasegawa's functions2012

    • Author(s)
      川崎雅人, 渚勝
    • Journal Title

      Technical reports of Math. Sci. Chiba Univ.

      Pages: 1-7

    • Related Report
      2013 Final Research Report
  • [Journal Article] Transforms on operator monotone functions2012

    • Author(s)
      川崎雅人, 渚勝
    • Volume
      arXiv:1206.5452
    • NAID

      130007833161

    • Related Report
      2013 Final Research Report
  • [Journal Article] Characterization of diagonality for operators2012

    • Author(s)
      伊藤隆, 渚勝
    • Journal Title

      Scientiae Math. Japon

      Volume: 75 Pages: 263-273

    • NAID

      130007663399

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Characterization of diagonality for operators2012

    • Author(s)
      伊藤 隆、渚 勝
    • Journal Title

      Scientiae Mathematicae Japonicae

      Volume: 75

    • NAID

      130007663399

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some operator monotone functions related to Petz-Hasegawa functions2012

    • Author(s)
      川崎雅人、渚 勝
    • Journal Title

      Technical Reports of Mathematical Sciences, Chiba University

      Volume: 28

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Order of operators determined by operator mean

    • Author(s)
      渚勝, 内山充
    • Journal Title

      Tohoku Math. J.

      Volume: (to appear)

    • NAID

      130007961972

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on rational operator monotone functions

    • Author(s)
      渚勝
    • Journal Title

      Scientiae Math. Japon.

      Volume: (to appear)

    • NAID

      130007643069

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Presentation] 微分による作用素の順序2014

    • Author(s)
      渚勝, 渡辺春香
    • Organizer
      日本数学会
    • Place of Presentation
      学習院大学
    • Year and Date
      2014-03-18
    • Related Report
      2013 Final Research Report
  • [Presentation] Szaboによる作用素単調関数2014

    • Author(s)
      渚勝, 和田州平
    • Organizer
      日本数学会
    • Place of Presentation
      学習院大学
    • Year and Date
      2014-03-18
    • Related Report
      2013 Final Research Report
  • [Presentation] Order of operators determined by operator mean2013

    • Author(s)
      渚勝, 内山充
    • Organizer
      作用素論研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2013-11-08
    • Related Report
      2013 Final Research Report
  • [Presentation] 作用素平均とその逆順序2013

    • Author(s)
      渚勝, 内山充
    • Organizer
      日本数学会
    • Place of Presentation
      愛媛大学
    • Year and Date
      2013-09-27
    • Related Report
      2013 Final Research Report
  • [Presentation] 作用素単調関数について2013

    • Author(s)
      渚勝
    • Organizer
      短期共同研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2013-02-04
    • Related Report
      2013 Final Research Report
  • [Presentation] 作用素単調関数について2013

    • Author(s)
      渚 勝
    • Organizer
      上越作用素環セミナー
    • Place of Presentation
      上越教育大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] 作用素単調関数について2013

    • Author(s)
      渚 勝
    • Organizer
      共同研究「量子化と作用素環」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Haagerupテンソル積と拡張されたHaagerupテンソル積2012

    • Author(s)
      伊藤隆, 渚勝
    • 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
      2012-11-23
    • Related Report
      2013 Final Research Report
  • [Presentation] 作用素の対角性の特徴付け2012

    • Author(s)
      伊藤隆, 渚勝
    • Organizer
      日本数学会
    • Place of Presentation
      九州大学
    • Year and Date
      2012-09-24
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
  • [Presentation] ある作用素単調関数について2012

    • Author(s)
      川崎雅人, 渚勝
    • Organizer
      日本数学会
    • Place of Presentation
      九州大学
    • Year and Date
      2012-09-19
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
  • [Presentation] Some operator monotone function2012

    • Author(s)
      渚勝
    • Place of Presentation
      Kyungpook National University, Korea
    • Year and Date
      2012-06-25
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Some operator monotone functions2012

    • Author(s)
      Masaru Nagisa
    • Organizer
      Positive Matrices and Operators: Recent developments and Advances
    • Place of Presentation
      Kyungpook National University (Korea)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Haagerupテンソル積と拡張されたHaagerup テンソル積2012

    • Author(s)
      渚 勝
    • Organizer
      作用素論・作用素環論研究集会
    • Place of Presentation
      大阪教育大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Order of operators determined by operator mean

    • Author(s)
      渚 勝
    • Organizer
      作用素論短期共同研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
  • [Presentation] Order of operators determined by operator mean

    • Author(s)
      渚 勝
    • Organizer
      日本数学会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] 微分による作用素の順序

    • Author(s)
      渡辺春香
    • Organizer
      日本数学会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Szabo による作用素単調関数

    • Author(s)
      和田州平
    • Organizer
      日本数学会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Annual Research Report
  • [Remarks] 改装中

    • URL

      http://www.math.s.chiba-u.ac.jp/~nagisa

    • Related Report
      2013 Final Research Report
  • [Remarks] 平成24年度教育研究実績報告

    • URL

      http://www.s.chiba-u.ac.jp/Edu_research/T_research/report/index_h24.html

    • Related Report
      2012 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

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