一类向后权位移的循环向量

CYCLIC VECTOR CF BACRWARD SHIFT

设T是权为{W_n}_0~∞的权位移。通常,T酉等价于由形式幂级数构成的函数空间H^2(β)上的乘子z:f→zf.本文证明,如果T是一个内射单侧权位移,适合r_1(T)=r(T)=1,如果f在单位圆盘的某邻域内解析,则要么f是T~*的循环向量,要么f含于T~*的有限维不变子空间.

Let T be a weighted shift with weights Wn As usually, T will be identified as mult -iplication by z on some function space H2 consisting of formal power series. It is shown in this paper that if r1 (T) =r(T) = 1, then for any function f(z) that is analystic in a neighbourhood of closes unit disc, either f(z) is a cyclic vector of T or f(z) is in some finite-dimensional invariant subspace of T .