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RESEARCHES ON SIMULTANEOUS UNITARY DILATIONS OF OPERATORS ON HILBERT SPACES

Hilbert空间算子联立酉扩张的研究

基本信息

批准号：
12640152
负责人：
OKAYASU Takateru
金额：
$ 2.18万
依托单位：
YAMAGATA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

项目摘要

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.

Takateru Okayasu，首席研究员，研究了Hilbert空间上算子元组的结构，这些算子元组本质上是g定和g半定的，是对正三角多项式系数模的最尖锐估计。另一方面，他得到了几个关于等距图的Korovkin型线性近似的结果，这些结果统一和推广了很久以前就知道的一些事实。川村晋三从概率论的角度研究了混沌动力系统。Takashi Sano研究了简单c -代数的具体包体，得到了Watatani指数、比率集和a -扩展的一些结果。Takahiro Mizuhara给出了由Morrey函数、bloch和Riesz势引起的h函数的弱分解定理，并研究了Morrey空间上Rieaz势与局部可积函数之间的对易子的条件。佐藤恩司研究了LCA群的洛伦兹空间上平移不变有界线性算子的结构。他还研究了正数上的一些Hankel变换算子与区间（0,π）上的Jacobi正交系统算子之间的关系。Muneo Cho和Kotaro Tanahashi研究了与次正规算子有密切关系的算子，如对数次正规算子，w次正规算子，像Furuta的1，Putunam的1等算子不等式，以及由于Taylor和Xia引起的算子谱，得到了许多有趣的结果。