拟相似算子的并谱图象与 Kato本性谱的连通成分

UNION SPECTRAL PICTURE OF QUASISIMILAR OPERATORS AND COMPONENTS OF KATO ESSENTIAL SPECTRA

本文给出拟相似算子并谱图象及其特性。文中推广了[2]的定理1,[3]的定理1.4和对 Fialkow 文[4]中定理3.11给一个新证明,进而给出三个:若 A,B 是拟相似(A～～B),Δ为σ_(?)(A)的一个连通成分,必有Δ∩σ_(?)(B)≠(?)的充要条件。举例说明:若A～～B,则σ_(?)·(A)的每个连通成分可不必与σ_(?)(B)相交。

In this paper we discuss the union spctral picture of quasisimilar opera-tors and its characteristics,we extend Theorem I in[2].Theorem 1.4 in[3]and give a new proof of Theorem 3.11 in[4].Then we obtain three necess-ary-sufficient conditions for Δ∩σ_K(B)≠(?) where A and B are quasisimilaroperators (A～～B)and Δis a component of σ_K(A).we give an example tosnow thar every Component of σ_K(A)doesn′t intersect σ_K(B).