赵广华.关于左移加权移位的循环向量[J].数学研究及应用,1984,4(3):1~6
关于左移加权移位的循环向量
On Cyclic Vectors of Backward Weighted Shifts
投稿时间:1981-10-04  
DOI:10.3770/j.issn:1000-341X.1984.03.001
中文关键词:  
英文关键词:
基金项目:
作者单位部门
赵广华 陕西师范大学 Shaanxi Normal University
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中文摘要:
      设{wn}1是一复的有界序列。l2上由T(x0,x1,x2,…)=(w1x1,w2x2,…)定义的算子T称为以{wn}1为权的左移加权移位。本文证明了T为循环算子的充要条件是{wn}1至多只有一项为零;讨论了某些特殊加权移位的循环向量;并指出[1]的有误之处。所得结果是[1]中结果的推广。
英文摘要:
      Let {wn}1 be a bounded sequence of complex numbers. The unique operator T on l2 defined by T(x0,x1,x2,…)=(w1x1,w2x2,w3x3,…) is called a backward weighted shift. In this paper, it is shown that T is cyclic if and only if {wn}1 has at most one term equal to zero; cyclic vectors of certain special weighted shifts are discussed; and it is also pointed out that there are something wrong in the contents of theorems in [1]. The results are extensions to those in [1].
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