文献类型：期刊文献

中文题名：About Operator Weighted Shift

英文题名：About Operator Weighted Shift

作者：Chun Lan JIANG[1];Yong Fei JIN[2];Zong Yao WANG[2]

机构：[1]Department of Mathematics, Hebei Normal University, Shifiazhuang 050016, P. R. China;[2]Department of Mathematics, East China University of Science and Technology, Shanghai 200237, P. R. China

年份：2007

卷号：23

期号：8

起止页码：1385

中文期刊名：Acta Mathematica Sinica,English Series

外文期刊名：数学学报（英文版）

收录：CSTPCD;;Scopus;CSCD:【CSCD2011_2012】；PubMed;

基金：Work partially supported by NNSFC

语种：英文

中文关键词：Operator weighted shift;Strongly irriducible operator;Similarity;Commutant;Jacobson radical

外文关键词：Operator weighted shift, Strongly irriducible operator, Similarity, Commutant, Jacobson radical

摘要：Abstract Let H be a complex seperable Hilbert space and ^（Jt^） denote the collection of bounded linear operators on H. For an operator in L（H）, rad{A}＇ denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}＇/rad{A}＇. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant is commutative.
Abstract Let H be a complex seperable Hilbert space and ^（Jt^） denote the collection of bounded linear operators on H. For an operator in L（H）, rad{A}＇ denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}＇/rad{A}＇. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant is commutative.