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2013 Fiscal Year Final Research Report

Study on operator inequalities based on various analytic methods

Research Project

  • PDF
Project/Area Number 23540215
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KOSAKI Hideki  九州大学, 数理(科)学研究科(研究院), 教授 (20186612)

Co-Investigator(Kenkyū-buntansha) WATATANI Yasuo  九州大学, 数理学研究院, 教授 (00175077)
Co-Investigator(Renkei-kenkyūsha) HIAI Fumio  東北大学, 名誉教授 (30092571)
SANO Takashi  山形大学, 理学部, 教授 (20250912)
Project Period (FY) 2011 – 2013
Keywords作用素平均 / 正定値関数 / 量子情報理論
Research Abstract

To get norm comparison results for operator means we have to check positive definiteness of ratios of relevant means. By computing Fourier transforms we have checked positive definiteness of a variety of ratios. We have also made use of the concept of infinite divisibility to establish this for some ratios whose explicit computations of Fourier transforms seem hopeless.
On the other hand, our technique was proved useful for study on completely positive maps appearing naturally in quantum information theory.

  • Research Products

    (8 results)

All 2014 2013 2012 2011

All Journal Article (7 results) (of which Peer Reviewed: 7 results) Presentation (1 results)

  • [Journal Article] C*-algebras associated with complex dynamical systems and backward orbit structure2014

    • Author(s)
      T.Kajiwara and Y.Watatani
    • Journal Title

      Complex Analysis and Operator Theory

      Volume: 8 Pages: 243-254

    • Peer Reviewed
  • [Journal Article] KMS states on finite graph C*-algebras2013

    • Author(s)
      T.Kajiwara and Y.Watatani
    • Journal Title

      Kyushu J. Math

      Volume: 67 Pages: 83-104

    • Peer Reviewed
  • [Journal Article] Families of completely positive maps associated with monotone metrics2013

    • Author(s)
      F.Hiai, H.Kosaki, D.Petz and M.B.Ruskai
    • Journal Title

      Linear Algebra Appl

      Volume: 439 Pages: 1749-1791

    • Peer Reviewed
  • [Journal Article] Trace Jensen inequality for self-adjoint operators in semi-finite von Neumann algebtras2013

    • Author(s)
      H.Kosaki
    • Journal Title

      Internat. J. Math

      Volume: 24 Pages: 1350075 (15)

    • Peer Reviewed
  • [Journal Article] Loewner matrices of matrix convex and monotone functions2012

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

      J. Math. Soc., Japan

      Volume: 64 Pages: 343-364

    • Peer Reviewed
  • [Journal Article] Positive definiteness of functions with applications to operator norm inequalities2011

    • Author(s)
      H.Kosaki
    • Journal Title

      Mem. Amer. Math. Soc

      Volume: 212 Pages: v + 80

    • Peer Reviewed
  • [Journal Article] C*-algebras associated with algebraic correspondences on the Riemann sphere2011

    • Author(s)
      T.Kajiwara and Y.Watatani
    • Journal Title

      J. Operator Theory

      Volume: 65 Pages: 427-449

    • Peer Reviewed
  • [Presentation] Infinite divisibility in study of operator means2011

    • Author(s)
      H. Kosaki
    • Organizer
      Seminare D'Anlysis Fonctionnelle, Universite de Franche-Comte
    • Place of Presentation
      Besancon, France
    • Year and Date
      20110900

URL: 

Published: 2015-07-16  

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