令H是无限维的Hilbert空间，B(H)是H上有界线性算子的全体构成的集合。称算子T ∈ B(H)满足Browder定理，若σ(T)\ σw(T)⊆π00(T)或σw(T)=σb(T)，其中 σ(T)，σw(T)，σb(T)分别表示算子 T 的谱集、Weyl 谱、Browder谱，π00(T)={λ∈ isoσ(T):0＜dimN(T-λI)＜∞}。借助新的谱集，给出有界线性算子及其函数满足Browder定理的等价条件。
Judgement of Browder's Theorem for Bounded Linear Operators and Their Functions
Let H be an infinite dimensional Hilbert space and B(H)be the algebra of all bounded linear operators on H.T ∈ B(H)satisfies the Browder's theorem if σ(T)\ σw(T)⊆π00(T)or σw(T)=σb(T),where σ(T),σw(T),σb(T)denote the spectrum,Weyl spectrum,Browder spectrum,and π00(T)={λ ∈ isoσ(T):0＜dimN(T-λI)＜∞}.In this paper,we establish for bounded linear operators and their functions the equivalent conditions for which Browder's theorem holds by a new spectrum.
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