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

On many approaches of the invariantsubspace problem in Hilbert spaces

Research Project

Project/Area Number 22540184
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

OHWADA Tomoyoshi  静岡大学, 教育学部, 教授 (50321386)

Co-Investigator(Kenkyū-buntansha) SAITO Kichi-suke  新潟大学, 自然科学系, 教授 (30018949)
WATATANI Yasuo  九州大学, 数理(科)学研究科(研究院), 教授 (00175077)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsinvariant subspace(不変部分空間) / Hilbert spaces(ヒルベルト空間) / analytic crossed products(解析的接合積) / factorization theorem / von Neumann algebra / invariant subspace / crossed product / analytic subalgebra / maximality / semigroup / Banach space / inequality / banach space
Research Abstract

The invariant subspace problem is the question that every bounded operator on a separable Hilbert space has a non-trivial invariant subspace. There has been a large amount of work on invariant subspaces, motivated by interest in the structure of non-self adjoint operators on Hilbert space. Our purpose is to investigate this problem on many ways; theory of operator algebras, Banach spaces and Hilbert spaces. And we succeeded in development of much theory relevant to the problem.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (53 results)

All 2012 2011 2010 Other

All Journal Article (27 results) (of which Peer Reviewed: 27 results) Presentation (26 results) (of which Invited: 1 results)

  • [Journal Article] Kolmogorov's factorization theorem for von Neumann algebras2012

    • Author(s)
      K. Nakade, T. OHWADAand K.-S. SAITO
    • Journal Title

      J. Math. Anal. Appl

      Volume: Vol. 401 Pages: 289-292

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Characterization of the intermediate values of the triangle inequality2012

    • Author(s)
      K. MINENO, Y. NAKAMURA and T. OHWADA
    • Volume
      Vol. 15
    • Pages
      1019-1035
    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Kolmogorov's factorization theorem for von Neumann algebras2012

    • Author(s)
      T. Ohwada
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 401 Pages: 289-292

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Characterization of the intermediate values of the triangle inequality2012

    • Author(s)
      K. Mineno
    • Journal Title

      Math. Inequal. Appl.

      Volume: 15 Pages: 1019-1035

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Dunkl-Williams inequality and the generalized operator version2012

    • Author(s)
      K-S. Saito
    • Journal Title

      International Series of Numerical Mathematics

      Volume: 161 Pages: 137-148

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] KMS states on finite graph C*-algebras2012

    • Author(s)
      T. Kajiwara
    • Journal Title

      Kyushu J. Math.

      Volume: -

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fundamental group of simple C*-algebras with unique trace II2011

    • Author(s)
      N. NAWATA and Y. WATATANI
    • Journal Title

      J. Funct. Analysis

      Volume: Vol. 260 Pages: 428-435

    • NAID

      120004951556

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Schatten p-norm inequalities related to an extended operator parallelogram law2011

    • Author(s)
      M. S. MOSLEHIAN, M. TOMINAGA and K.-S. SAITO
    • Journal Title

      Linear Algebras and Applications

      Volume: Vol. 435 Pages: 823-829

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On λ-commuting operators2011

    • Author(s)
      L.Zhang, T.Ohwada, M.Cho
    • Journal Title

      International Mathematical forum

      Volume: 6 Pages: 1685-1690

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On extension of the sharp triangle inequalities2011

    • Author(s)
      T.Ohwada, K.Mineno, Y.Nakamura
    • Journal Title

      Banach and Function Space III

      Volume: 3 Pages: 441-451

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Another aspect of triangle inequality2011

    • Author(s)
      K.-S.Saito, R.An, H.Mizuguchi, K.Mitani
    • Journal Title

      ISRN Math.Anal.

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Schatten p-norm inequalities related to an extended operator parallelogram law2011

    • Author(s)
      M.S.Moslehian, M.Tominaga, K.-S.Saito
    • Journal Title

      Linear Algebras and Applications

      Volume: 435 Pages: 823-829

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Extremal structure of the set of absolute normalized norms on R^2 and the James constant2011

    • Author(s)
      N.Komura, K.-S.Saito, K.Mitani
    • Journal Title

      Applied Math. Computation

      Volume: 217 Pages: 10035-10048

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On sharp triangle inequalities in Banach spaces and its applications2011

    • Author(s)
      K.-S.Saito, K.Mitani
    • Journal Title

      Banach and Function Spaces III

      Volume: 3 Pages: 295-304

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some geometrical constants of absolute normalized norms on R^22011

    • Author(s)
      H.Mizuguchi, K.-S.Saito
    • Journal Title

      Ann.Funct.Anal.

      Volume: 2 Pages: 22-33

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The monotonicity of absolute normalized norms on C^n2011

    • Author(s)
      K.Mitani, K.-S.Saito, N.Komura
    • Journal Title

      Nihonkai Math.J

      Volume: 22 Pages: 91-102

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fundamental group of simple C^*-algebras with unique trace II2011

    • Author(s)
      N.Nawata, Y.Watatani
    • Journal Title

      J.Funct.Analysis

      Volume: 260 Pages: 428-435

    • NAID

      120004951556

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sharp mean triangle inequality2010

    • Author(s)
      M.Fujii, M.Kato, K.-S.Saito, T.Tamura
    • Journal Title

      Math.Inequal.Appl.

      Volume: 13 Pages: 743-752

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Extremal structure of the set of absolute normalized norms on R^2 and the von Neumann-Jordan constant2010

    • Author(s)
      N.Komuro, K.-S.Saito, K.Mitani
    • Journal Title

      J.Math.Anal.Appl.

      Volume: 370 Pages: 101-106

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniform non-l_1 ^n-ness of ψ-direct sums of Banach spaces X+ψY2010

    • Author(s)
      M.Kato, K.-S.Saito, T.Tamura
    • Journal Title

      J.Nonlinear Analysis and Convex Analysis

      Volume: 11 Pages: 13-33

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Dunkl-Williams type inequality for absolute value operator2010

    • Author(s)
      K.-S.Saito, M.Tominaga
    • Journal Title

      Linear Alg.Appl.

      Volume: 432 Pages: 3258-3264

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on Clarkson's inequality in the real case2010

    • Author(s)
      H.Mizuguchi, K.-S.Saito
    • Journal Title

      J.Math.Inequal.

      Volume: 4 Pages: 129-132

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Toeplitz-composition C^*-algebras for certain finite Blaschke products2010

    • Author(s)
      H.Hamada, Y.Watatani
    • Journal Title

      Proc.Amer.Math.Soc.

      Volume: 138 Pages: 2113-2123

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fundamental group of simple C^*-algebras with unique trace2010

    • Author(s)
      N.Nawata, Y.Watatani
    • Journal Title

      Adv.Math.

      Volume: 225 Pages: 307-318

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a continuous mapping and sharp triangle inequalities

    • Author(s)
      T.Ohwada
    • Journal Title

      Inequalities and Applications 2011

      Volume: (印刷中)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Characterization of the intermediate values of the triangle inequality

    • Author(s)
      K.Mineno, Y.Nakamura, T.Ohwada
    • Journal Title

      Math.Inequal.Appl.

      Volume: (印刷中)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] KMS states on finite-graph C^*-algebras

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

      Kyushu J.Math.

      Volume: (印刷中)

    • NAID

      130003364801

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] How to calculate James constant of Banach spaces?2012

    • Author(s)
      K.-S. SAITO
    • Organizer
      The foruth International symposium on Banach and Function Spaces
    • Place of Presentation
      九州工業大学
    • Year and Date
      2012-09-13
    • Related Report
      2012 Final Research Report
  • [Presentation] 無限次元ヒルベルト空間上の Kronecker quiver の brick ヒルベルト表現2012

    • Author(s)
      M. ENOMOTO and Y. WATATANI
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-29
    • Related Report
      2012 Final Research Report
  • [Presentation] Von Neumann Jordan定数の凸性について2012

    • Author(s)
      K.-S.Saita, N.Komura, K.Mitani, R.Tanaka
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京理科大学,東京都
    • Year and Date
      2012-03-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] Several geometric constants of absolute normalized norm on R^22012

    • Author(s)
      H.Mizuguchi, K.-S.Saito
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京理科大学,東京都
    • Year and Date
      2012-03-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] 無限次元ヒルベルト空間上のKronecker quiver のbrickヒルベルト表現2012

    • Author(s)
      M.Enomoto, Y.Watatani
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京理科大学,東京都
    • Year and Date
      2012-03-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] 自己相似写像から作られるC^*-環のコアの行列表現2012

    • Author(s)
      T.Kajiwara, Y.Watatani
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京理科大学,東京都
    • Year and Date
      2012-03-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] On the reverses of the triangle inequality in inner product spaces2012

    • Author(s)
      T.Ohwada
    • Organizer
      Colloquium of the department of Math., Universidad Complutense de Madrid
    • Place of Presentation
      Complutense University, Madrid, Spain
    • Year and Date
      2012-02-12
    • Related Report
      2011 Annual Research Report
  • [Presentation] Von Neumann Jordan定数について2011

    • Author(s)
      K.-S.Saito
    • Organizer
      作用素論・作用素環論研究集会
    • Place of Presentation
      琉球大学,沖縄県
    • Year and Date
      2011-11-05
    • Related Report
      2011 Annual Research Report
  • [Presentation] Skewness and geometrical constants for Banach spaces2011

    • Author(s)
      K.Mitani, K.-S.Saito, Y.Takahashi
    • Organizer
      日本数学会秋期分科会
    • Place of Presentation
      信州大学,長野県
    • Year and Date
      2011-09-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] バナッハ空間のskew定数について2011

    • Author(s)
      K.Mitani, K.-S.Saito, Y.Takahashi
    • Organizer
      非線形解析学と凸解析学の研究
    • Place of Presentation
      京都大学数理解析研究所,京都府
    • Year and Date
      2011-08-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] On reverse of the triangle inequality in normed linear spaces2011

    • Author(s)
      T. OHWADA
    • Organizer
      The 7-th International conference on Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      Pukyong National University (韓国)
    • Year and Date
      2011-08-03
    • Related Report
      2012 Final Research Report
  • [Presentation] On reverses of the triangle inequality in normed linear spaces2011

    • Author(s)
      T.Ohwada
    • Organizer
      The 7-th International conference on Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      Pukyong National University, Busan, Korea
    • Year and Date
      2011-08-03
    • Related Report
      2011 Annual Research Report
  • [Presentation] On the James constant of extrem absolute norms on R^2 and their dualnorms2011

    • Author(s)
      N.Komura, K.-S.Saito, K.Mitani
    • Organizer
      The 7-th International conference on Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      Pukyong National University, Busan, Korea(招待講演)
    • Year and Date
      2011-08-03
    • Related Report
      2011 Annual Research Report
  • [Presentation] How to caluculate the geometrical constants of Banach spaces2011

    • Author(s)
      K.-S.Saito
    • Organizer
      The 7-th International conference on Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      Pukyong National University, Busan, Korea(招待講演)
    • Year and Date
      2011-08-03
    • Related Report
      2011 Annual Research Report
  • [Presentation] On a continuous mapping constructed by the triangle inequalities and its applications2011

    • Author(s)
      大和田智義
    • Organizer
      バナッハ空間論の研究とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2010 Annual Research Report
  • [Presentation] On the James constant of absolute norms on R^22011

    • Author(s)
      小室直人、斎藤吉助、三谷健一
    • Organizer
      バナッハ空間論の研究とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2010 Annual Research Report
  • [Presentation] バナッハ空間のskewnessについて2011

    • Author(s)
      三谷健一、斎藤吉助
    • Organizer
      バナッハ空間論の研究とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2010 Annual Research Report
  • [Presentation] Sharp triangle inequalities in Banach spaces and the recent results2010

    • Author(s)
      K.Mitani, K.-S.Saito
    • Organizer
      実解析学シンポジウム
    • Place of Presentation
      九州工業大学
    • Year and Date
      2010-11-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] On a continuous mapping and sharp triangle inequalities2010

    • Author(s)
      大和田智義
    • Organizer
      The Conference on Inequalities and Applications '10
    • Place of Presentation
      Hiajduszoboszlo, Hungary
    • Related Report
      2010 Annual Research Report
  • [Presentation] The sharp triangle inequalities and its applications to the geometry of Banach spaces2010

    • Author(s)
      K.-S.Saito
    • Organizer
      The Conference on Inequalities and Applications '10
    • Place of Presentation
      Hajduszoboszlo, Hungary
    • Related Report
      2010 Annual Research Report
  • [Presentation] absolute normの集合の端点構造につい2010

    • Author(s)
      三谷健一、斎藤吉助、小室直人
    • Organizer
      作用素論における非可換構造の研究とその応用
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2010 Annual Research Report
  • [Presentation] Absolute normの単調性とその応用2010

    • Author(s)
      斎藤吉助、三谷健害、小室直人
    • Organizer
      非線形解析学と凸解析学の研究
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2010 Annual Research Report
  • [Presentation] Beckner の不等式とそのBanach 空間への応用について

    • Author(s)
      斎藤吉助
    • Organizer
      日本数学会
    • Place of Presentation
      京都大学(京都府)
    • Related Report
      2012 Annual Research Report
  • [Presentation] 有限次元ノルム空間の構造について

    • Author(s)
      田中亮太朗
    • Organizer
      日本数学会
    • Place of Presentation
      京都大学(京都府)
    • Related Report
      2012 Annual Research Report
  • [Presentation] 有限次元ノルム空間の構造と直交基底について

    • Author(s)
      田中亮太朗
    • Organizer
      実解析学シンポジウム
    • Place of Presentation
      茨城大学(茨城県)
    • Related Report
      2012 Annual Research Report
  • [Presentation] How to calculate James constant of Banach spaces?

    • Author(s)
      斎藤吉助
    • Organizer
      The foruth Internatinal symposium on Banach and Function Spaces
    • Place of Presentation
      九州工業大学(福岡県)
    • Related Report
      2012 Annual Research Report
    • Invited

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi