关于拟相似算子的谱及本性谱的几点注记

A Note on Spectra and Essential Spectra of Quasisimilar Operators

本文给出在边界相等条件下,可分Hilbert空间上两个拟相似算子的谱及本性谱相等的充要条件。举例说明边界相等而两个拟相似算子的谱及本性谱可以不相等。最后讨论了两个拟相似双侧带权移位算子本性谱相等的充分条件。推广了L.R.Williams在[6]中的结果。

This article deals with some criteria for the equality of essential spectra of two quasisimilar operators under the assumption that the boundaries of their spectra are the same. An example is given to show that it may happen that the spectra and the essential speetra of two equasisimilar operators may be not equal even though the boundaries of their spectra are the same. Some full conditions for equality of essential spectra of two quasisimilar bilateral weighted shift operators also are given and william's results in [6] are generalized.