【作者】 原江涛；

【导师】 杨长森；

【作者基本信息】 河南师范大学 ， 基础数学， 2005， 硕士

【摘要】 本篇论文中,我们主要研究与Furuta不等式及Aluthge变换相关的一些算子类,重点讨论wF(p,r,q)类,F(p,r,q)类等的性质.第一章首先引入与Furuta不等式及Aluthge变换相关的wF(p,r,q)类算子,继而讨论其性质,诸如该类算子的特征,该类算子间及与其他相关算子类间的相互关系,该类算子成为正规算子的条件,该类算子幂的性质等.第二章研究与Furuta不等式及Aluthge变换相关的一些算子类诸如F(p,r,q)类,wF(p,r,q)类及(p,r,q)-仿正规类等的一些性质.第一节到第三节可看作第一章第三节的延续.第四节给出了p-亚正规算子的一个与F(p,r,q)类及(p,r,q)-仿正规类相关的特征.第五节对对数-亚正规算子和p-亚正规算子的Aluthge变换性质作了进一步讨论.更多还原

【Abstract】 In this paper, we shall study classes of operators associated with Furuta inequality and Aluthge transformation, mainly class wF(p,r,q), class F(p,r,q) and so on. Next, we shall give several results on p-hyponormal and log-hyponormal operators.In ChapterⅠ, firstly, we introduce class wF(p,r,q) operators which is associated with Furuta inequality and generalized Aluthge transformation. Secondly, we shall show several properties of this class, such as its characterizations, inclusion relations, normality, powers and so on.In ChapterⅡ, we shall study classes of operators associated with Furuta inequality and Aluthge transformation, such as class F(p,r,q), class wF(p,r,q) and (p,r,q)-paranormal operators and so on.§2.1-§2.3 can be regarded as further discussion of§1.3 of ChapterⅠ.§2.4 is to show a characterization of p-hyponormal operators via class F(p, r, q) and (p, r, q)-paranormal operators.§2.5 is to discuss Aluthge transformation of p-hyponormal and log-hyponormal operators.更多还原