算子的拟正规性及亚正规性  

Quasi-normality and Hyponormality of operators

作　　者：葛斌[1] 钟凤远[2] 

机构地区：[1]哈尔滨工程大学理学院 [2]哈尔滨理工大学数学系

出　　处：《黑龙江大学自然科学学报》2009年第3期303-305,310,共4页Journal of Natural Science of Heilongjiang University

摘　　要：设H是复可分H ilbert空间。L(H)是H上有界线性算子全体构成的C*代数。讨论算子的拟正规性与亚正规性的关系,并以单侧加权移位算子为例证明了并非所有的亚正规算子是拟正规的。证明了紧的亚正规算子是拟正规的。Let H be a complex, separable Hilbert space. L（H） denotes the C^＊ algebra of all bounded linear operators acting on H. Firstly, The relation between the quasi - normal and hyponormal operators is investigated. Then it is proven by an example unilateral weighted shift operator that hyponormality can not imply quasi -normality. Fi- nally, it is shown that compact hyponormal operators are quasi -normal.

关 键 词：拟正规算子 亚正规算子 完全非正规算子 

分 类 号：O177.1[理学—数学]