关于Lambert权位移的若干性质

ON SOME PROPERTIES OF THE LAMBERT'S WEIGHTED SHIFTS

设A是Hilbert空间H上的内射算子,对非零向量f∈H,称带有权序列的加权移位算子为Lambert权位移,记作A_f.文中刻划了Lambert权位移的若干性质.证明了,若A是H上的内射亚正规算子,则每一个A_f,也是亚正规的.如果存在非零向量f∈H,使适合:i)存在子列,{m_i}_(i=1)~∞使x_m_i≠0;ii)极限则x是向后的Lambert权位移T_(A.f)的循环向量.又设T是带权序列{W_x}_1~∞的向后权位移,{W_x}_1~∞单调递减趋于零,对x={x_m}∈l^2,若有子列{x_n_i}_(i=1)~∞使数列有界或者数列有界,则x是T的循环向量.

Let A be an injective operator on Hilbert space //, for nonzero vector f in II, we call that A, is a Lamber's weighted if Af is a weighted shift operator with weight sequenceSome properties of the Lambert's weighted shifts are characterized. It is shown that every A, is hyponormal operator if A is an injective hyponormal . Assume that there exists nonzero vector /in //, such that supsatisfies. i) exists subsequence {m,), such thatii) limthen i is a cyclic vector of backward Lambert's shift TA, and it is proved, in addition, that for T is a backward weighte shift with weight sequence {w} , {ai,} is monotone decreasing and w-0, for x= {xm}, if there exists subsequence {x} such that or sequenceis bounded, then a; is a cyclic vector of T.