【摘要】 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。更多还原

【Abstract】 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.更多还原