A类算子的谱性质

The Spectrum Properties of Class A Operator

主要讨论了A类算子谱的性质.若T是A类算子且ker kerT T*,则Weyl谱的谱映射定理及本质近似点谱的谱映射定理成立;若T是A类算子且ker kerT T*且S与T拟相似,则α-Browder′s定理对f(S)成立,其中f∈H(σ(S)).

This artical is devoted to introduce the spectrum properties of class A operator.If T is a class A operator and ker kerT T＊,then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum,and if T is a class A operator and ker kerT T＊,S and T quasi similarity,then α-Browder′s theorem holds for every f∈H（σ（S））.