算子权移位的强不可约性  

Strong irreducibility of operator weighted shifts

作　　者：葛斌[1] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2007年第3期286-290,共5页Journal of Natural Science of Heilongjiang University

摘　　要：讨论以可逆算子作为权序列的无穷重的算子权移位的强不可约性.这里给出了三个充分条件:设S是以{Wk}∞k=1(其中Wk∈L(H),k∈Z)为权序列的算子权移位.(1){Wn-1Wn--11…W1-1AW1W2…Wn}n∞=1有界蕴含A=λI.(或A=λI+Q,Q是严格上三角算子,λ∈C);(2){Wn-1Wn--11…W1-1AW1W2…Wn}n∞=1有界蕴含σ(A)是单点集;(3){Wn-1Wn--11…W1-1AW1W2…Wn}∞n=1有界蕴含A是强不可约的.最后给出了利用上述条件判定S强不约性的例子.The strong irreducibility of infinite multiplicity operator weighted shifts with weighted sequence of inverse operators are discussed. It obtains that three sufficient conditions： let S be an operator weighted shift with weighted sequence{Wk}^∞k=1then（1） is bounded implies that {Wn^-1Wn-1^-1…W1^-1AW1W2…Wn}n^∞=1 is strict upper triangular operator,λ∈C;（2）{Wn^-1Wn-1^-1…W1^-1AW1W2…Wn}n^∞=1 is bounded implies that σ Q is a single point set; and （3） {Wn^-1Wn-1^-1…W1^-1AW1W2…Wn}^∞n=1is bounded implies that A is strongly irreducible. At the last two examples are given, which verify the strong irreducibility of S by these conditions mentioned above.

关 键 词：无穷重 加权移位算子 强不可约 

分 类 号：O177.1[理学—数学]