| Project/Area Number |
12640152
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | YAMAGATA UNIVERSITY |
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Principal Investigator |
OKAYASU Takateru YAMAGATA UNIVERSITY, DEPARTMENT OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (60005775)
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| 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)
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| Project Period (FY) |
2000 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2001: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2000: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | ESSENTIALLY MNORMAL OPERATORS / POSITIVE TRIGONOMETRIC POLYNOMIALS / CHAOS DYNAMICAL SYSTEMS / GROUPOID C-ALGEBRAS / KAC ALGEBRAS / COMMUTATORS / LORENTZ SPACES / HYPONORMAL OPERATORS / groupuid C-algebra / Loventz空間 / 耳正規作用素 / カオス写像 / 位相的グルーポイド / Morrey空間 / ハンケル変換 / Aluthge変換 / 古田不等式 / Essentially definite operators / Simultaneous unitary dilation / 可換標準的同型 / Lorentz空間 / p-hyponormal operators / log-hyponormal operators |
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| 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.
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