Banach空间中单侧加权移位的谱性质和拟相似

Spectral Properties of Unilateral Weighted Shifts and Quasisimilarity in Banach Space

本文给出了Banach空间中单侧加权移位的谱性质,证明了当对应的基是无条件基时,两个单侧加权移位的拟相似性、稠值域相似性、相似性是等价的,推广并加强了已有的有关结果。

This article gives spectral properties of unilateral weighted shifts in a Banach space and prove that when the associated bases are unconditional bases, the quasisimilarity, dense-range-similarity and similarity for two unilateral Weighted hifts are equivalent. These results generalize and strengthen the related conclusions which have been proved by other mathematicians.