拟- k -仿正规算子的一个注解

数学物理学报 ›› 2014, Vol. 34 ›› Issue (4): 917-924.

拟- k -仿正规算子的一个注解

左飞|申俊丽

河南师范大学数学与信息科学学院河南新乡 453007

收稿日期:2012-08-09 修回日期:2013-11-29 出版日期:2014-08-25 发布日期:2014-08-25
基金资助:
国家自然科学基金 (11201126)、河南师范大学青年基金(2013QK01)和河南省教育厅科学技术研究重点项目(14B110008)资助.

A Note on Quasi-{\boldmath k-paranormal Operators

ZUO Fei, SHEN Jun-Li

College of Mathematical and Informational Science, Henan Normal University, Henan Xinxiang 453007

Received:2012-08-09 Revised:2013-11-29 Online:2014-08-25 Published:2014-08-25
Supported by:
国家自然科学基金 (11201126)、河南师范大学青年基金(2013QK01)和河南省教育厅科学技术研究重点项目(14B110008)资助.

摘要/Abstract

摘要：

设T是复希尔伯特空间H上的有界线性算子, 若对任意的x∈H, T满足
||^Tk+2x||||T_x||^k≥||T²x||^k+1,
则称T为拟- k -仿正规算子, 其中k为正整数. 该文给出了拟- k -仿正规算子的一些性质, 如拟- k -仿正规算子是极, 作为此性质的应用, 证明了拟- k -仿正规算子满足Weyl定理.

关键词: 拟- k -仿正规算子, 极, Weyl定理

Abstract:

Let T be a bounded linear operator on a complex Hilbert space H. T is said to be a quasi-k-paranormal operator if
||^Tk+2x||||T_x||^k≥||T²x||^k+1for all x∈H,
where k is a positive integer. Some basic properties of quasi-k-paranormal operators are shown. In particular, quasi-k-paranormal operator is polaroid, as an application, we obtain that Weyl's theorem holds for the class of quasi-k-paranormal operators.

Key words: Quasi-k-paranormal operators, Polaroid, Weyl´s theorem

中图分类号:

47A10

左飞, 申俊丽. 拟- k -仿正规算子的一个注解[J]. 数学物理学报, 2014, 34(4): 917-924.

ZUO Fei, SHEN Jun-Li. A Note on Quasi-{\boldmath k-paranormal Operators[J]. Acta mathematica scientia,Series A, 2014, 34(4): 917-924.

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