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Research of inequalities of matrix algebra using analytic method

Research Project

Project/Area Number 09640143
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionHOKKAIDO UNIVERSITY OF EDUCATION

Principal Investigator

OSADA Masayuki (1998)  Sapporo College, Assistant Professor, 教育学部札幌校, 助教授 (10107229)

大久保 和義 (1997)  北海道教育大学, 教育学部・札幌校, 教授 (80113661)

Co-Investigator(Kenkyū-buntansha) KOMURO Naoto  Asahikawa College, Assistant Professor, 教育学部旭川校, 助教授 (30195862)
NISIMURA Jun-ichi  Sapporo College, Assistant Professor, 教育学部札幌校, 助教授 (00025488)
HASEGAWA Izumi  Sapporo College, Professor, 教育学部札幌校, 教授 (50002473)
SAKURADA Kuninori  Sapporo College, Professor, 教育学部札幌校, 教授 (30002463)
長田 正幸  北海道教育大学, 教育学部・札幌校, 助教授 (10107229)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 1998: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1997: ¥1,900,000 (Direct Cost: ¥1,900,000)
Keywordsunitary rho dilation / operator radius / Schur product / Holder type inequality / Holder型不等式 / ヒルベルト空間 / 有界線形作用素 / 数域半径 / 作用素ノルム
Research Abstract

1 It is considered many (quasi-)norms on the space of all n*n complex matrices. The rho radius omega_<rho>(.) is one of them. In this research, we will characterize this norm in the case of 2 * 2 matrices by using the theory of complex functions, and apply it to calculation of the rho-radius for some matrices. The main result is the following : Let a, b *D : ={z*C||z|<less than or equal> 1}. Then for rho <greater than or equal> A=[a c 0 b] is a rho-contraction if a
|c|<@D12@>D1+|a-b|<@D12@>D1 <less than or equal> inf|<@D7{rho+(rho)azeta}{rho+(-rho)bzeta}-ab|zeta<@D12@>D1(/)5 pizet
2 Besides of usual mulpiplication, entrywise product (it is called Schur product) or matrices is considered. We had Holder type inequality for p-radius with respect to Schur product as following : Let 0<rho0<rho1<*. Then for any non-negative matrices A, B,
omega_<rho>(A^<(alpha)> o B^<(1-alpha>) <less than or equal> omega_<rho0>(A)^<alpha>_<rho1>(B)^<1-alpha> (0<alpha<1 ; alphazeta0+(1-alpha)zeta1).

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (10 results)

All Other

All Publications (10 results)

  • [Publications] T.Ando and K.Okubo: "Ho^<・・>lder-type inequalities associated with operator radii and Schur products" Linear and Multilinear Algebra. 43. 53-61 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Nakazi and K.Okubo: "ρ-contraction and 2×2 matrix" Linear Algebra and its Application. 283. 165-169 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Nakazi and K.Okubo: "Generalized numerical radius and unitary ρ-dilation" Mathematica Japonica. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Ando and K.Okubo: "Holder-type inequalities associated with operator radii and Schur products" Linear and Multilinear Algebra. 43. 53-61 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Nakazi and K.Okubo: "rho-contraction and 2*2 matrix" Linear Algebra and its Application. 283. 165-169 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Nakazi and K.Okubo: "Generalized numerical radius and unitary rho-dilation" Mathematica Japonica. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Ando and K.Okubo: "Holder-type inequalities associated with operator radii and Schur products" Linear and Multilinear Algebra. 43. 53-61 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Nakazi and K.Okubo: "ρ-contraction and 2×2 matrix" Linear Algebra and its Application. 283. 165-169 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Nakazi and K.Okubo: "Generalized numerical radius and unitary ρ-dilation" Mathematica Japonica. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Nakazi and K.Okubo: "P-Contraction and 2×2 matrix" Linear Alg.and Application.

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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