弱亚正规算子的正规性

J4 ›› 2013, Vol. 48 ›› Issue (09): 68-72.

弱亚正规算子的正规性

杨桦1,2,常欢3,吉国兴2

1.安阳工学院数理学院, 河南安阳 455000; 2.陕西师范大学数学与信息科学学院, 陕西西安 710062;
3.安阳开发区高中, 河南安阳 455000

收稿日期:2012-04-26 出版日期:2013-09-20 发布日期:2013-09-25
作者简介:杨桦(1982- ),女,助教,研究方向为算子代数. Email: huayang2006@126.comp
基金资助:
国家自然科学基金资助项目(10571114);陕西省自然科学基础研究计划资助课题(2005A1)

The normality of p-w-hyponormal operators

YANG Hua1,2, CHANG Huan3, JI Guo-xing2

1. School of Science, Anyang Institute of Technology, Anyang 455000, Henan, China;
2. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China;
3. Anyang Hitech Zone High School, Anyang 455000, Henan, China

Received:2012-04-26 Online:2013-09-20 Published:2013-09-25

摘要/Abstract

摘要：

设T∈B(H),如果对某个p>0都有||p≥|T|p≥|*|p,则称T是p-弱亚正规算子。本文主要研究了p-弱亚正规算子T和它的Aluthge变换的拟正规性和次正规性之间的关系,证明了是拟正规算子当且仅当T是拟正规算子。最后,举例得到了存在非次正规的p弱亚正规算子T而是次正规的。

关键词: p-弱亚正规算子;正规算子;拟正规算子;次正规算子

Abstract:

Let T∈B(H). If ||p≥|T|p≥|*|p for some p>0, then T is p-w-hyponormal. The quasinorma and subnormal relation of T and its Aluthge transform are studied. It is proved that is quasinormal if and only if T is quasinormal. An example that there exists a non subnormal p-w-hyponormal operator T and subnormal is given.

Key words: p-w-hyponormal operator; normal operator; quasinormal operator; subnormal operator

杨桦1,2,常欢3,吉国兴2. 弱亚正规算子的正规性[J]. J4, 2013, 48(09): 68-72.

YANG Hua1,2, CHANG Huan3, JI Guo-xing2. The normality of p-w-hyponormal operators [J]. J4, 2013, 48(09): 68-72.

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