拟相似算子本性谱的连通成分

On Connected Components of the Essential Spectrum of Quasisimilar Operators

设A和B是拟相似算子,△是Wolf本性谱σc（B）的任一个连通成分。本文证明了△∩σ■（A）∩σ■（B）≠φ及△∩（σ■（A）∩σ■（B））≠φ。并证明了若△σK（B）的一个连通成分,则△∩（σF（A）∩σF（B））≠φ等价于△∩（σ■（A）∩σ■（B））≠φ,进而给出△∩σ■（A）∩σ■（B）≠φ的充要条件,其中σK（T）=σ■（T）∩σ■（T）,σ■（T）=σK（T）\(P’∞（T）0∪P’∞∞（T）0),P’∞（T）={λ∈C:v（T-λ）-μ（T-λ）=±∞},P∞∞’（T）={λ∈C:v（T-λ）=μ（T-λ）=∞}。

Suppose A, B are quasisimilar operators, △ is any connected component of Wolf essential spectrum σ_e(B). It is shown in this article that A∩σ_e(A)∩ σ_e(B) ≠φ and . It is provec also that given any component △ of σ_κ(B), is equivalent to and then some equivalent conditions for are given. In the above;