算子的拟相似性与本质谱的性质

Quasisimilarity of Operators and Properties of the Essential Spectrum

设算子A和B拟相似,本文通过算子谱的精密结构的分析,给出了算子A的Wolf本质谱、Kato本质谱、Weyl本质谱以及右本质谱的连通分支与算子B的Wolf本质谱的某些子集的相交关系,并肯定地回答了L．A．Fialkow在文献[3]中提出的一个问题．

Let A and B be quasisimilar operators. By means of the analysis of the precise constitution of spectrum of operators, this paper gives the intersection relations between the components of the Woff essential spectrum, the Kato essential spectrum, the Weyl essential spectrum, the right essential spectrum of operator A and some subsets of the Woff essential spectrum of operator B, and positively answers the question of L.A.Fialkow in [3].