算子的拟相似与(Q)类算子

Quasisimilarity of Operators and (Q) Operators

本文引进定义于L(H)上的集值函数β(S)和(Q)类算子(指本质谱含于其一切拟相似算子的本质谱的算子),用β(S)刻划 (Q)类算子的特征;证明(Q)类算子范围广泛,次可分解算子(包括次标量算子,M-亚正常算子,半亚正常算子等等)是其中的一部分;(Q)类算子在L(H)中稠密.

In this paper, we introduce the conceptions S∈ (Q) S∈ L(H) with σe(S) C σe(T) for every operator T quasisimilar to S, β(S) = {λ∈C : a neighbourhood U of λ such that (S -z) ○(V,H) is closed for every neighbour hood V of λ, V U}, characterize (Q) operators by means of β(S) and show that the family of (Q) operators includes many familiar operators (such as subdecompasable, M-hyponormal, semi-hyponormal operators, etc.) and is norm-dense in L(H).