算子的拟相似与Kato本质谱的连通分支

Quasisimilarity of Operators and Components of Kato Essential Spectrum

设算子A和B拟相似,τ是Kato本质谱σ_K(B)的连通分支,本文研究τ∩σ_K(A)≠φ的充分条件和必要条件以及τ与σ_B(A)的某些子集的相交关系。

Let A and B be quasisimilar operators and lat τ be a component of Kato essenial spectrum σ_K(B). In this article we study the sufficient conditions and necessary conditions for τ∩σ_K(A)≠φ, and discuss the properties of certain subsets of σ_B(A) concerning their intersection relations with τ. Also some results about the family of operators, (QQ)= {S∈B(H): for every T quasisimilar to S, every component of σ_K(T) intersects σ_K(B) and every component of σ_K(S) intersects σ_K(T)} are introduced, including the density in B(H) of (QQ)_(qt).