加权移位算子的非游荡性

Nonwandering Property of Weighted Shifts

以构造的方式,研究了lp(1≤p<∞)空间上的加权移位算子B,当其权序数满足一定条件时,具有非游荡性;证明了它经过一恒等算子扰动后,仍可保持这种特性;进而得到了Hilbert空间上的任一有界线性算子关于非游荡算子的分解理论.

With a constructive technique, the nonwandering property ot welgnteo shift D was cnaracterized on sequence space l^p （1≤ p 〈 ∞） , when its weighted sequences satisfies certain conditions. Meanwhile, the perturbation of these operators by an identity operator is still nonwandering. Further- more, every bounded linear operator on Hilbert space can be decompositioned into nonwandering operator.