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Research of operator inequalities and log-hyponormal operators

算子不等式和对数次正规算子研究

基本信息

批准号：
15540180
负责人：
TANAHASHI Kotaro
金额：
$ 2.05万
依托单位：
Tohoku Pharmaceutical University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540180/
关键词：
log-hyponormal operator p-hyponormal operator (p, k) -quasihyponormal operator class A(s, t) operator Fuglede-Putnam theore Weyl' s theorem p-quasihyponormal operator class A operator 作用素不等式 log-hyponormal作用素 class A作用素 class A(s,t)作

项目摘要

The aim of this research is to develop the theory of operator inequality and study the properties of log-hyponormal and related classes of operators. The main results due to K.Tanahashi and A.Uchiyama is as follows ; If an operator A is paranormal or class A(s,t), then Riesz idempotent corresponding to an isolated point of spectrum is self-adjoint if the point is not 0. If A is a class A(s,t) operator, then the Riesz idempotent is identical to the Riesz idempotent of its Aluthge transform. A tensor product of A, B is log-hyponormal (resp.class A(s,t)) if and only if both A and B are log-hyponormal (resp.class A(s,t)). Fugled-Putnam type theorem holds for p-hyponormal, p-quasihyponormal operators. Fugled-Putnam type theorem holds for injective (p,k)-quasihyponormal operators. Fugled-Putnam type theorem holds for log-hyponormal operators or class Y operators. Algebraically paranormal operators satisfies Wyle's theorem. Putnam type inequality holds for class A operators. M.Takemoto, A.Uch … More iyama and L.Zsido proved that any convex subsets of Rn or Cn is σ-convex. This gives a useful role for the arguments of the numerical ranges of Hilbert space operators. Y.Miura proved the non-commutative L2 version of a Kadison theorem on the decomposition theorem of Jordan isomorphisms in the theory of operator algebras using the notion of completely positive maps on the Hilbert space associated with a standard von Neumann algebra. He introduced in his joint works the partial order on the set of all bound ed linear operators on a Hilbert space with a selfdual cone in the sense of positive maps on selfdual cones, and investigated several properties of this order for the important cones such as powers of operators and the difference with the usual order defined on all hermitian operators. He also as joint worksdealed with the convergency problem of a recursive sequences defined by x_{n+l}=f(x_{n-1},x_n), and gave the affirmative answer more simply and generally than the results of Stevic and his fellows, and applied to a model for competing species in biomathematics. Less

本研究的目的是发展算子不等式理论并研究对数次正规算子和相关类算子的性质。 K.Tanahashi 和 A.Uchiyama 的主要结果如下：如果算子 A 是超自然算子或 A(s,t) 类算子，则对应于谱孤立点的 Riesz 幂等如果该点不为 0，则该点是自伴的。如果 A 是 A(s,t) 类算子，则 Riesz 幂等与其 Aluthge 变换的 Riesz 幂等相同。 A、B 的张量积是对数次正态的（resp.class A(s,t)），当且仅当 A 和 B 都是对数次正态的（resp.class A(s,t)）。 Fugled-Putnam 型定理对于 p 次正规、p 拟次正规算子成立。 Fugled-Putnam 型定理对于单射 (p,k)-拟次正规算子成立。 Fugled-Putnam 类型定理适用于对数次正规运算符或 Y 类运算符。代数超自然算子满足怀尔定理。 Putnam 型不等式适用于 A 类运算符。 M.Takemoto、A.Uch ... More iyama 和 L.Zsido 证明了 Rn 或 Cn 的任何凸子集都是 σ 凸的。这为希尔伯特空间算子的数值范围的参数提供了有用的作用。 Y.Miura 使用与标准冯·诺依曼代数相关的希尔伯特空间上的完全正映射的概念，证明了算子代数理论中乔丹同构分解定理的 Kadison 定理的非交换 L2 版本。他在他的联合著作中介绍了具有自对偶锥体的希尔伯特空间上所有有界 ed 线性算子集合上的偏序，并研究了重要锥体的该阶数的几个性质，例如算子的幂以及与所有 Hermitian 算子上定义的通常阶数的差异。他还联合研究了由x_{n+l}=f(x_{n-1},x_n)定义的递归序列的收敛问题，并给出了比Stevic及其同事的结果更简单和更普遍的肯定答案，并应用于生物数学中的竞争物种模型。较少的