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Research of operator inequality and spectrum using computer

Research Project

Project/Area Number 14540190
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

CHO Muneo  Kanagawa University, Faculty of Engineering, 工学部, 教授 (10091620)

Co-Investigator(Kenkyū-buntansha) FURUTA Takayuki  Hirosaki University, Emerutus Professor, 名誉教授 (40007612)
HURUYA Tadasi  Niigata University, Faculty of Education and Human Science, 教育人間科学部, 教授 (90018648)
YAMAZAKI Takeaki  Kanagawa University, Faculty of Engineering, 工学部, 講師 (60333150)
Project Period (FY) 2002 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2004: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsHilbert space / trace formula / principal function / operator inequality / Shannon inequality / hyponormal operator / Aluthge transform / polar decomposition / operator / joint spectrum / hyponormal / n-tuple / trace
Research Abstract

Under the research project with title "Research of operator inequality and spectrum using computer", Takayuki Furuta (emerutus professor of Hirosaki University), Tadasi Huruya (Professor of Niigata University), Takeaki Yamazaki (Kanagawa University) and Muneo Cho (Kanagawa University) studied for three years. In this period, we invited V.Muller (Professor of Czech Academy), Andrzej Soltysiak (Professor of Adam Mickiewicz University), Woo Young Lee (Professor of Seoul University), Il Bong Jung (Professor of Kyungpook National University) and E.Albrecht (Professor of Universitat des Saarlandes) and studied this problem with them. Cho and Huruya studied principal functions started by M.Krein and studied continuously by J.Helton, R.Howe, R.Carey, J.Pincus, D.Xia and M.Putinar, who studied it in case of hyponormal operators and semi-hyponormal operators. We extended it in case of p-hyponormal operators and showed that the principal function of the Aluthge transformation is same the original one. We made 23 papers about these results. These have been published or will be published, recently. Furuta studied operator inequalities and got characterizations of chaotic order and generalized Kantorovich constant. He also applied these to Information Theory. He wrote 16 papers about these results. These have been published or will be published, recently. Yamazaki studied spectrum of operators. He got a spectrum-invariant transformation from class A to hyponormal operators. Also he studied numerical ranges by Aluthge transformation. He wrote 10 papers about these results. These have been published or will be published, recently. By this support, we wrote 49 papers. We express our cordial thanks for this Grant.

Report

(4 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (26 results)

All 2005 2004 Other

All Journal Article (13 results) Publications (13 results)

  • [Journal Article] Relations between principal functions of p-hyponormal operators2005

    • Author(s)
      長 宗雄, 古谷 正
    • Journal Title

      J.Math.Soc.Japan 57

      Pages: 605-618

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Relations between principal functions of p-hyponormal operators2005

    • Author(s)
      M.Cho, T.Huruya
    • Journal Title

      J.Math.Soc.Japan Vol.57

      Pages: 605-618

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Trace formulae of p-hyponormal operators2004

    • Author(s)
      長 宗雄, 古谷 正
    • Journal Title

      Studia Math. 161

      Pages: 1-18

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Mosaic and principal functions of log-hyponormal operators2004

    • Author(s)
      長 宗雄, 古谷 正, 山崎文明
    • Journal Title

      Integr.Equat.Oper.Th. 48

      Pages: 295-304

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Isolated points of spectrum of (p,k)-quasihyponormal operators2004

    • Author(s)
      長 宗雄, 内山 敦, 棚橋浩太郎
    • Journal Title

      Linear Algebra & Appl. 382

      Pages: 221-229

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Trace formulae of p-hyponormal operators2004

    • Author(s)
      M.Cho, T.Huruya
    • Journal Title

      Studia Math Vol.161

      Pages: 1-18

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Mosaic and principal functions of log-hyponormal operators2004

    • Author(s)
      M.Cho, T.Huruya, T.Yamazaki
    • Journal Title

      Integr.Equat.Oper.Th. Vol.48

      Pages: 295-304

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Isolated points of spectrum of (p, k)-quasihyponormal operators2004

    • Author(s)
      M.Cho, A.Uchiyama, K.Tanahashi
    • Journal Title

      Linear Algebra & Appl. Vol.382

      Pages: 221-229

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Mosaic, and principal functions of log-hyponormal operators2004

    • Author(s)
      長 宗雄, 古谷 正, 山崎丈明
    • Journal Title

      Integr.Equat.Oper.Th. 48

      Pages: 295-304

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Isolated points of spectrum of (p,k)-quasihyponormal operators2004

    • Author(s)
      長 宗雄, 棚橋浩太郎, 内山 敦
    • Journal Title

      Linear Alg.Appl. 382

      Pages: 221-229

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Parametric extensions of Shannon inequality and its reverse one in Hilbert space operators2004

    • Author(s)
      古田孝之
    • Journal Title

      Linear Alg.Appl. 381

      Pages: 219-235

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Convergence of logarithmic trace inequalities via generalized Lie-Trotter formulae2004

    • Author(s)
      古田孝之
    • Journal Title

      Linear Alg.Appl. 396

      Pages: 353-372

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On polar decomposition of the product of Aluthge transformation and related results2004

    • Author(s)
      山崎丈明, 伊藤公智, 柳田昌宏
    • Journal Title

      J.Operator Theory 51

      Pages: 303-319

    • Related Report
      2004 Annual Research Report
  • [Publications] K.Cho, A.Soltysiak, T.Yamazaki: "On approximate point joint spectrum of p-hyponomal and log-hyponormal operators"Commentationes Math.. 63. 33-41 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Cho, T.Huruya: "Aluthge transformations and invariant subapaces of p-hyponormal operators"Hokkaido Math.J.. 32. 445-450 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Cho, T.Huruya: "Riemann-Hilbert problem for operators associated with hyponormal operators and increasing functions"Int.J.Pure Applied Math.. 9. 145-151 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Cho, J.I.Lee: "p-Hyponormality is not translation-invariant"Proc.Amer.Math.Soc.. 131. 3109-3111 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Yamazaki, M.Yanagida: "Relations between two operator inequalities and their applications to paranormal operators"Acta Sci.Math.(Szeged). 69. 377-389 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Ando, T.Yamazaki: "The iterated Aluthge transforms of a 2-by-2 matrix converge"Linear Algebra Appl.. 375. 299-309 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 長宗雄, 古谷正, R.Curto: "N-tuples of operators satisfying σ_T(AB)=σ_T(BA)"Linear Algebra Appl.. 341. 291-298 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 長宗雄, 棚橋浩太郎: "Isolated point of spectrum of p-hyponormal, log-hyponormal operators"Integral Equations Operator Theory. 43. 379-384 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 長宗雄, W.Y.Lee, R.Curto: "Triangular Toepliz contractions and Cowen's sets for analytic polynomials"Proc. Amer. Math. Soc.. 130. 3597-3604 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 古田孝之: "A proof of an order preserving inequality"Proc. Japan Acad. Ser. A. 78. 26 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 山崎丈明: "An expression of spectral radius via Aluthge transformation"Proc. Amer. Math. Soc.. 130. 1131-1137 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 山崎丈明: "On numerical range of the Aluthge transformation"Liner Algebra Appl.. 341. 111-117 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 古田孝之: "もっとMathematicaで数学を"培風館. 150 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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