代数κ-拟--A算子的谱

THE SPECTRUM OF ALGEBRAICALLY K-QUASI-*-A OPERATOR

证明了若T是代数k-拟-＊-A算子，则T是polaroid．作为此性质的应用，证明了若T或T^＊是代数k-拟-＊-A算子，则f（T）满足Weyl定理；若T^＊是代数k-拟-＊-A算子，则f（T）满足a—Weyl定理，其中f∈H（σ（T））．

In this paper, it is proven that if T is an algebraically k-quasi-＊-A operator, then T is polaroid. As its applications, it is shown that if T or T^＊ is an algebraically k-quasi-＊-A operator, then Weyl＇s theorem holds for f（T）; if T^＊ is an algebraically k-quasi-＊-A operator, then a-Weyl＇s theorem holds for f（T）, where f ∈ H（σ（T））.