加权N移位的谱理论

Spectral Theory of Weighted N Shifts

本文在〔1〕的基础上进一步研究了加权N移位算子的各种谱分解性质,其主要结果是:(1)我们给出了加权N移位算子T和它的共轭算子T~*具有单值扩张性的几个充要条件;(2)对于加权N移位算子的局部谱,我们给出了一个估计式;(3)对于可分解加权N移位算子,我们给出了一系列等价命题。

On the basis of reference 〔1〕some spectral decomposition properties of weighted N shift operators were studied. The main results are that (1) For weighted N shift operators and their adjoint operators we give several sufficient and necessary conditions for them to have the single valued extension property; (2) We give an estimating formula for local spectrums of weighted N shift operators; (3) We give several equivalent conditions for decomposable weighted N shift operators.