• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

SCHWARZ NORMS IN OPERATOR ALGEBRAS AND CONTRACTIONS, AND ITS APPLICATIONS TO DIFFERENTIAL OPERATORS

Research Project

Project/Area Number 09640200
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

UCHIYAMA Mitsuru  FUKUOKA UNIVERSITY OF EDUCATION,FACULTY OF EDU,PROFESSOR, 教育学部, 教授 (60112273)

Co-Investigator(Kenkyū-buntansha) HARA Takuya  FUKUOKA UNIVERSITY OF EDUCATION,FACULTY OF EDU,ASSOCIATE PROFESSOR, 教育学部, 助教授 (50263984)
FUKUTAKE Takayoshi  FUKUOKA UNIVERSITY OF EDUCATION,FACULTY OF EDU,PROFESSOR, 教育学部, 教授 (60036887)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1998: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1997: ¥1,400,000 (Direct Cost: ¥1,400,000)
KeywordsOperator monotone function / Lowner-Heinz inequality / positive definite operator / norm / operator / matrix / determinant / Korovkin theory / Pick 関数 / 作用素単調関数 / Korovkinの定理 / C^*-環 / 作用素不等式 / 数域半径 / シュワルツノルム
Research Abstract

The research results which we have gotten with a support of GRANT TN AID for SEIENTIFIC RESEARCH (C) are 5 published papers, 3 accepted papers and I submitted paper. The content of them are as follows :
1. For non-negative operators (or matrices) A, B, and for an operator nonotone function f, we had
llf (A) f (B) ll * f (ROO<>llABll)^2
Especially, for the norms of products of logarithmic funtions we had
lllog (1 A) log (1+ B) ll * log (1+ ROO<>llABll)^2
Moreover these are extended to the case of real number powers, so it may be called Minkowski-type inequality. Furthur we investigated and showed that similar Minkowski-type inequality holds for determinants.
Mathematical Inequality and Appl.Vol.1(2)(1998)279-284.
2. Furuta extended the Heinz-Kato Inequality. We extended it as follows :
For operator monotone functions f(t), g(t) >0, T(fg/t)(ITI) is well defined for every T and satisfies T(fg/t)(ITI)x, y ) * (f(ITI)x, x)(g(ITI )y.y) for all vectors x, y
Proc. Amer.Math. Soc.
3. We studied Korovkin theory in C^*-algebras. We found a new inequality whch is very useful to study Korovkin theory. By making use of it, we made clear the the proofs of known theorems and got new Korovkin sets.
Mathinatishe Zeitshrift
4. The function f is called an operator monotone function if for operators A, B
0* f(A) * f(B) whenever 0* A * B
We showed that if f is an operator monotone function and if f is not rational, then f is strongly monotone.

Report

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

    (27 results)

All Other

All Publications (27 results)

  • [Publications] M.Uchiyama: "Numerical ranges of elements of involutive Banach algebras" Archiv der Mathematik. 69. 314-318 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Uchiyama: "Real analytic interpolation functions" Bulletin of Fukuoka Univ.of Education. 47. 9-16 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Uchiyama: "Norms and determinants of products of logarithmic functions" Math. Inequal.and Appl.1. 279-284 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Hara,M.Uchiyama,S.Takahashi: "A refinement of Various Mean Inequalities" J.Inequal.Appl.2. 387-395 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Hara: "Monotonicity of the inverses and operators" Bulletin of Fukuoka Univ.of Education. 47. 1-7 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Uchiyama: "Furthur Extensin of Heinz-Kato-Furuta Inequality" Proc.Amer.Math.Soc.(印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Uchiyama: "Korovkin-type theorems for Schwarz maps and operator monotone functions" Math.Z.(印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Uchiyama: "Some exponential operator inequalities" Mathematical Inequalities and Appl.(印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Uchiyama: "Numerical ranges of elements of involutive Banach algebras" Archiv der Mathematik. vol.69. 314-318 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Uchiyama: "Real analytic interpolation functions" Bulletin of Fukuoka Univ.of Education. vol.47. 9-16 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Uchiyama: "Norms and determinants of products of logarithmic functions" Math.Inequal.and Appl.Vol.1. 279-284 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Hara, M.Uchiyama, S.Takahashi: "A refinement of Various Mean Inequalities" J.Inequal.Appl.Vol.2. 387-395 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Hara: "Monotonicity of the inverses and operators" Bulletin of Fukuoka Univ.of Education. Vol.47. 1-7 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Uchiyama: "Furthur Extensin of Heinz-Kato-Furuta Inequality" Proc.Amer.Math.Soc.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Uchiyama: "Korovkin-type theorems for Schwarz maps and operator monotone functions in C^*-algebras" Math.Z.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Uchiyama: "Some exponential operator inequalities" Mathematical Inequalities and Appl.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Uchiyama.: "Norms and determinants of products of logarithmic" Mathematical Inegualities & Applications. 1巻・2号. 279-284 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Hara,M.Uchiyama: "A retinement of Vari'ous Mean Inegualities" Journal of Inequalities and Applications. 2巻. 387-395 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Uchiyama: "Further Extension of Heinz-Kato-Furuta Ineguality" Proc.American Math.Soc.校正済み.

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Uchiyama: "Korovkin-type theorems for Schwarz maps" Mathematishe Zeitshrift. 校正済み.

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Uchiyama: "Some exponential operator inequalities" Mathematical Inequalities & Applications. 受理.

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Uchiyama: "Numerical ranges of elements of involutive Banach algebras" Archiv der Mathematik(Birkhauser). 69巻. 314-318 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Uchiyama: "Real analytic wave interpolation functions" 福岡教育大紀要. 47巻3号. 9-16 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Uchiyama: "Heinz-Kato-Furuta lnequalitty" Proc,Amer.Math.SOC.(受理).

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Uchiyama: "Norms and determinants of products of logarithmic" Mathematical Inequalities & Applications. (印刷中).

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Hara,M.Uchiyama: "Arefinement of various mean inequalities" Journal of inequalities and application. (受理).

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Hara: "Monotonicity of the inverses and operators" 福岡教育大学紀要. 47巻・3号. 1-7 (1998)

    • Related Report
      1997 Annual Research Report

URL: 

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

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi