本质正规算子的模小紧相似

Similarity Small Module Compact of Essentially Normal Operators

本文证明了一类本质正规算子Ａ＇（Ω＇；１）（Ｔ∈Ａ＇（Ω＇；１），如果Ｔ满足（１）Ｔ，Ｔ｜Ｈ（Ｔ）分别是本质正规算子；（２）σ（Ｔ）＝Ω，ρＦ（Ｔ）∩σ（Ｔ）＝Ω；（３）ｉｎｄ（Ｔ－λ）＝－１，ｎｕｌ（Ｔ－λ）＝０，λ∈Ω＇；（４）σ（Ｔ｜Ｈ（Ｔ））是一完全集，这里Ω＇是一连通的解析Ｃａｕｃｈｙ域， Ｈｌ（Ｔ）＝ Ｖ｛ｋｅｒ（Ｔ－λ）＊：λ∈ρｒｓ－Ｆ（Ｔ）｝是模小紧相似的．

In this paper, we prove a class of essentially normal operators A'(Ω'; 1) (T ∈ A'(Ω'; 1), if T satisfies: (1) T, T|H(T) are essentially normal, respectively; (2) σ(T) = Ω', ρF(T) ∩σ(T)=Ω'; (3) ind(T-)(λ) = -1, nul(T) -λ) = 0, λ ∈Ω '; (4) σ(T|H(T)) is a perfet set, where Ω' is connected analtic Cauchy domain, Hl(T)=V{ker(T - λ)*: λ∈ρrs-F(T)} are similiar small module compact.