About Operator Weighted Shift  

作　　者：Chun Lan JIANG Yong Fei JIN Zong Yao WANG 

机构地区：[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

出　　处：《Acta Mathematica Sinica,English Series》2007年第8期1385-1390,共6页数学学报（英文版）

基　　金：Work partially supported by NNSFC

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.

关 键 词：Operator weighted shift Strongly irriducible operator SIMILARITY COMMUTANT Jacobson radical 

分 类 号：O17[理学—数学]