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The construction ofthe spectral theory on quantum deformed operators and its application to quantum physics

Research Project

Project/Area Number 20540178
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

OTA Shoichi  九州大学, 大学院・芸術工学研究院, 教授 (70107176)

Co-Investigator(Kenkyū-buntansha) 井上 淳  福岡大学, 理学部, 教授 (50078557)
Co-Investigator(Renkei-kenkyūsha) INOUE Atushi  福岡大学, 理学部, 教授 (50078557)
CHO Muneo  神奈川大学, 工学部, 教授 (10091620)
Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsunbounded operator / deformed operator / q-normal operator / Hilbert space / subnormal operator / q-normal / q-circular
Research Abstract

A kind of spectral theory of q-deformed operators in a Hilbert space is needed so that unbounded representations of quantum algebras are analyzed. This work is devoted toinvestigating a q-normal operator in a Hilbert space, compared with a standard spectral measure and the spectral decomposition for a normal operator in a Hilbertspace. It is shown that, if a positive number q is smaller than 1, every q-normal operator in a Hilbert space is extended to a standard normal operator in a possibly larger Hilbert space.

Report

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

    (28 results)

All 2012 2011 2010 2009 2008 Other

All Journal Article (17 results) (of which Peer Reviewed: 15 results) Presentation (11 results)

  • [Journal Article] Tanahashi, Invertible weighted shift operators which are m-isometries2012

    • Author(s)
      M. Cho, S. Ota, K
    • Journal Title

      Proceedings of American Mathematical society

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tanahashi, On m-isometric operators2012

    • Author(s)
      M Cho, S. Ota, K
    • Journal Title

      Glasnik Matematicki

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On m-isometric operators2012

    • Author(s)
      S.Ota, et al
    • Journal Title

      Glasnik Matematicki

      Volume: (印刷中)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Commutativity to within scalars on Banach space2011

    • Author(s)
      M. Cho, R. Harte, S. Ota
    • Journal Title

      Functional Analysis, Approximation and Computation

      Volume: vol.3 Pages: 69-77

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Commutativity to within scalars on Banach space2011

    • Author(s)
      S.Ota, et al
    • Journal Title

      Functional Analysis, Approximation and Computation

      Volume: 3 Pages: 69-77

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Operator equation AB=BA2010

    • Author(s)
      M. Cho, B. P. Duggal, R. Harte, S. Ota
    • Journal Title

      International Mathematical Forum

      Volume: vol.5 no.53 Pages: 2629-2637

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] q-deformed circularity for an unbounded operator in Hilbert space2010

    • Author(s)
      S. Ota
    • Journal Title

      Colloquium Mathematicum

      Volume: vol.120 Pages: 191-199

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Circular作用素について2010

    • Author(s)
      太田昇一
    • Journal Title

      数理解析研究所講究録

      Volume: 1678巻 Pages: 128-133

    • NAID

      40017112198

    • Related Report
      2011 Final Research Report
  • [Journal Article] 非有界作用素と量子群に現れる変形作用素について2010

    • Author(s)
      太田昇一
    • Journal Title

      数学

      Volume: 62巻 Pages: 40-56

    • NAID

      10026792279

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Operator equation AB=BA2010

    • Author(s)
      M.Cho, B.P.Duggal, R.Harte, S.Ota
    • Journal Title

      International Mathematical Forum vol.5 no.53

      Pages: 2629-2637

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] q-deformed circularity for an unbounded operator in Hilbert space2010

    • Author(s)
      S.Ota
    • Journal Title

      Colloquium Mathematicum vol.120

      Pages: 191-199

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Circular作用素について2010

    • Author(s)
      太田昇一
    • Journal Title

      数理解析研究所講究録 1678巻

      Pages: 128-133

    • NAID

      40017112198

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] 非有界作用素と量子群に現れる変形作用素について2010

    • Author(s)
      太田昇一
    • Journal Title

      数学 62巻

      Pages: 40-56

    • NAID

      10026792279

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] q-deformed circularity for an unbounded operator in Hilbert space2010

    • Author(s)
      S.Ota
    • Journal Title

      Colloquium Mathematicum

      Volume: 120 Pages: 191-199

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Operator equation AB=λBA2010

    • Author(s)
      S.Ota, et al
    • Journal Title

      International Mathematical Forum

      Volume: 5 Pages: 2629-2637

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 非有界作用素と量子群に現れる変形作用素について2010

    • Author(s)
      太田昇一
    • Journal Title

      数学 62

      Pages: 40-56

    • NAID

      10026792279

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Invertible weighted shift operators which are m-isometries

    • Author(s)
      S.Ota, et al
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: (掲載決定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] m-isometric operator s2011

    • Author(s)
      長宗雄
    • Organizer
      数理解析研究所研究集会
    • Place of Presentation
      京都大学
    • Year and Date
      2011-11-14
    • Related Report
      2011 Final Research Report
  • [Presentation] m-isometric operators2011

    • Author(s)
      長宗雄(代表)
    • Organizer
      数理解析研究所研究集会
    • Place of Presentation
      京都大学
    • Year and Date
      2011-11-14
    • Related Report
      2011 Annual Research Report
  • [Presentation] Topics related to deformed operators with parameters2010

    • Author(s)
      太田昇一
    • Organizer
      Functions and Operators
    • Place of Presentation
      Jagiellonian University,ポーランド
    • Year and Date
      2010-06-25
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Topics related to deformed operators with parameters2010

    • Author(s)
      S.Ota
    • Organizer
      Functions and Operators
    • Place of Presentation
      Jagiellonian University, Krakow, ポーランド
    • Year and Date
      2010-06-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Circular作用素について2009

    • Author(s)
      太田昇一
    • Organizer
      数理解析研究所研究集会
    • Place of Presentation
      京都大学
    • Year and Date
      2009-10-30
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Circular 作用素について2009

    • Author(s)
      太田昇一
    • Organizer
      数理解析研究所研究集会
    • Place of Presentation
      京都大学
    • Year and Date
      2009-10-30
    • Related Report
      2009 Annual Research Report
  • [Presentation] A quantum deformed operator, International conference on infinite particle2008

    • Author(s)
      太田昇一
    • Organizer
      Systems and complex systems
    • Place of Presentation
      Kazimierz,ポーランド
    • Year and Date
      2008-09-22
    • Related Report
      2011 Final Research Report
  • [Presentation] A quantum deformed operator2008

    • Author(s)
      太田昇一
    • Organizer
      International conference on infinite particle Systems and complex systems
    • Place of Presentation
      Kazimierz,ポーランド
    • Year and Date
      2008-09-22
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] A quantum deformed operator2008

    • Author(s)
      太田 昇一
    • Organizer
      International conference on infinite particle Systems and complex systems
    • Place of Presentation
      Kazimierz, Poland
    • Year and Date
      2008-09-22
    • Related Report
      2008 Annual Research Report
  • [Presentation] A quantum deformed operator and its applications2008

    • Author(s)
      太田昇一
    • Organizer
      The Fifth International Conference of Applied Mathematics and Computing
    • Place of Presentation
      Plovdiv,ブルガリア
    • Year and Date
      2008-08-16
    • Related Report
      2011 Final Research Report
  • [Presentation] A quantum deformed operator and its applications2008

    • Author(s)
      太田 昇一
    • Organizer
      The Fifth International Conference of Applied Mathematics and Computing
    • Place of Presentation
      Plovdiv, Bulgaria
    • Year and Date
      2008-08-16
    • Related Report
      2008 Annual Research Report

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

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