On Cyclic Vectors of Backward Weighted Shifts
Received:October 04, 1981  
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Zhao Guanghua Shaanxi Normal University Shaanxi Normal University
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Abstract:
      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].
Citation:
DOI:10.3770/j.issn:1000-341X.1984.03.001
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