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2002 Fiscal Year Final Research Report Summary

RESEARCHES ON SIMULTANEOUS UNITARY DILATIONS OF OPERATORS ON HILBERT SPACES

Research Project

Project/Area Number 12640152
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionYAMAGATA UNIVERSITY

Principal Investigator

OKAYASU Takateru  YAMAGATA UNIVERSITY, DEPARTMENT OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (60005775)

Co-Investigator(Kenkyū-buntansha) MIZUHARA Takahiro  YAMAGATA UNIVERSITY, DEPARTMENT OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (80006577)
SANO Takashi  YAMAGATA UNIVERSITY, DEPARTMENT OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCE, ASSOCIATE PROFESSOR, 理学部, 助教授 (20250912)
KAWAMURA Shinzo  YAMAGATA UNIVERSITY, DEPARTMENT OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (50007176)
CHO Muneo  KANAGAWA UNIVERSITY, DEPARTMENT OF MATHEMATICICS, PROFESSOR, 工学部, 教授 (10091620)
SATO Enji  YAMAGATA UNIVERSITY, DEPARTMENT OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (80107177)
Project Period (FY) 2000 – 2002
KeywordsESSENTIALLY MNORMAL OPERATORS / POSITIVE TRIGONOMETRIC POLYNOMIALS / CHAOS DYNAMICAL SYSTEMS / GROUPOID C-ALGEBRAS / KAC ALGEBRAS / COMMUTATORS / LORENTZ SPACES / HYPONORMAL OPERATORS
Research Abstract

Takateru Okayasu, the head investigator, studied the structure of tuples of operators on a Hilbert space which are essentially G-definite and G-semidefinite, the sharpest estimates for the moduli of coefficients of positive trigonometric polynomials. He, on the other hand, got several results on the Korovkin type linear approximation for isometric maps by conractive maps, that unify and gerenalize some facts which have known from long ago.
Shinzo Kawamura studied chaotic dynamical systems in the view points of the probability theory. Takashi Sano studied concrete inclusions of simple C-algebras, getting some results ahout the Watatani index, ratio sets and A-extensions. Takahiro Mizuhara showed the weak factorization theorem for H-functions due to Morrey functions, bloch and Riesz potential, and investigated conditions for the commutator, on Morrey spaces, between the Rieaz potential and a locally integrable function to he bounded. Enji Sato studied the structure of translation invariant bounded linear operators on Lorentz spaces of LCA groups. Also he studied the relation between some operators of Hankel transforms on the positive numbers and the operators of Jacobi orthogonal system on the interval (0,π). Muneo Cho and Kotaro Tanahashi studied operators in a near relation to hyponormal operators, e.g., log-hyponormal ones, w-hyponormal ones, operator inequalities like Furuta's one, Putunam's one, and etc, and spectra of operators due to Taylor and to Xia, having got many interesting results.

  • Research Products

    (32 results)

All Other

All Publications (32 results)

  • [Publications] Takateru Okayasu, Yasunori Ueta: "Estimates for moduli of coefficients of positive trigonometric polynomials"Scientiae Math. Japonicae. 56(1). 115-122 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tomoko Hachiro, Takateru Okayasu: "Some theorems of Korovkin type"Studia Math.. 115(2). 131-143 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Kawamura: "Chaotic maps on a measure space and the behavior of the orbit of a state"Tokyo Jour. Math. 24(2). 509-533 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Sano: "On Commuting Canonical endomuphisma endomorphisms of subfactor"Jour. Math. Soc. Japan. 55. 131-141 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Mizuhara: "Commutators of singular integral operators on Morrey spaces with some growth functions"Proc. 2nd ISAAC Cong.. 1. 65-73 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] O.Hatori, E.Sato: "Decompositions of measures on compact abelian groups"Tokyo Jour. Math. 24. 13-18 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Muneo Cho, Tadasi Huruya and Young Ok Kim: "A note on w-hyponormal operators"Journ. Ineq. Appl.. 7(1). 1-10 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Muneo Cho and Kotaro Tanahashi: "Isolated point of spectrum of P-hyponormal, log-hyponormal operators"Integr. Eq. Op. Theory. 43. 379-384 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Uchiyama and K. Tanahashi: "On Riesz idempotent of class A operators"Math. Ineq. Appl.. 5(3). 291-298 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kotaro Tanahashi: "Putnam's inequality for log-hyponormal operators"To appear in Intege. Eq. Op. Theory.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Tanahashi, A. Uchiyama and M. Uchiyama: "On Schwarz type inequalities"To appear.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takatru Okayasu: "The Lowner-Heinz inequality in Banach ^*-algebras"Glasgow Math. Journ.. 42. 243-246 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takateru Okayasu and Yasunori Ueta: "On essentialliy definite, and semidefinite tuples of operators"Sci. Math. Japon. 56(1). 107-113 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takateru Okayasu and Yasunori Ueta: "Estimates for moduli of coefficients of positive trigonometric polynomials"Sci. Math. Japon.. 56(1). 1115-1122 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tomoko Hachiro and Takateru Okayasu: "Some theorems of Korovkin type"Stud. Math.. 155(2). 131-143 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Shinzo Kawamura: "Chaotic maps on a measure space and the behavior of the orbit of a state"Tokyo Journ. Math.. 24(2). 509-533 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi Sano: "On commuting canonical endomorphisms of subfactors"Journ. Math. Soc. Japan. 55(1). 131-141 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yasuo Komori and Takahiro Mizuhara: "Notes on commutators and Morry spaces"To appear in Hokkaido Math. Journ..

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Osamu Hatori and Enji Sato: "Decompositions of measures on compact abelian groups"Tokyo Journ. Math.. 24(1). 13-18 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Muneo Cho, Takayuki Furuta, Jun Ik Lee and Woo Young Lee: "A folk theorem on Furuta inequality"Sci. Math.. 3(3). 299-231 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Cho, T. Huruya and M. Itoh: "Spectra of completely log-hyponormal operators"Integr. Eq. Op. Theory. 37(1). 1-8 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Cho, I. H. Jeon and J. I. Lee: "Joint spectra of doubly commuting n-tuples of operators and their Althge transforms"Nihonkai Math. Journ.. 11(1). 87-96 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Muneo Cho, In Ho Jeoo and Jun Ik Lee: "Spectral and structural properties of log-hyponormal operators"Glasgow Math. Journ.. 42(3). 345-350 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Muneo Cho, Tadasi Huruya, Youg Ok Kim and Jun Ik Lee: "A note on real parts of some serni-hyponormal operators"Acta Sci. Math. (Szeged). 66. 731-736 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Cho, B. P. Duggal and W. Y. Lee: "Putnam's inequality of doubly commuting n-tuples for log-hyponormal operators"Math. Royal Irish Acad.. 100A(2). 163-169 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Cho, R. E. Cruto, T. Huruya and W. Zelazko: "Cartesian form of Putnam's inequality for doubly commuting hyponormal n-tuples"Indiana Univ. Math. Journ.. 49(4). 1437-1447 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Cho and T. Huruya: "Square of w-hyponormal operators"Integr. Eq. Op. Theory. 39. 413-420 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Muneo Cho and Kotaro Tanahashi: "Angular cutting for log-hyponormal operators"Integr. Eq. Op. Theory. 40. 383-390 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Muneo Cho, Tadasi Huruya and Masuo Itoh: "Singular integral models for log-hyponormal operators and the Riemann-Hilbert problem"Internat. Journ. Math., Game Theory, and Alg.. 11(6). 55-69 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Cho, I. H. Joen, I. B. Jung, J. I. Lee and K. Tanahashi: "Joint spectra of n-tuples of generalized Althge transformations"Rev. Roumaine Math. Pures Appl.. 46(6). 725-730 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Muneo Cho, and Kotaro Tanahashi: "Spectral relations for Althge transform"Sci. Math. Japon. 55(1). 77-83 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Muneo Cho, Raul E. Cruto and Tadasi Huruya: "n-Tuples of operators satisfying σ_T(AB) = σ_T(BA)"Lin. Alg. Its Appl.. 341. 291-298 (2002)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2004-04-14  

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