算子函数演算的Wey1定理

摘要

设H为复的无限维可分的Hilbert空间,B(H)为H上的有界线性算子的全体.若σ(T)＼σw(T)=π00(T),则称T∈B(H)满足Weyl定理,其中σ(T)和σw(T)分别表示算子T的谱和Weyl谱,700(T)表示谱集中孤立的有限重特征值的全体.首先给出了Hilbert空间上有界线性算子Weyl-Kato分解的定义,并由Weyl-Kato分解的性质定义了一种新的谱集,利用该谱集刻画了算子函数演算满足Weyl定理的充要条件.%Let H be an infinite dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H.An operator T∈ B(H) is said to satisfy Weyl's theorem if σ(T) σw (T) =π00 (T),where σ(T) and σw (T) denote the spectrum and Weyl spectrum of operator T respectively,and π00 (T) denotes the set of all isolated eigenvalues of finite multiplicity.In this note,it is given that the definition of the Weyl-Kato decomposition of a bounded linear operator on Hilbert space.Using the new spectrum defined by the definition of the Weyl-Kato decomposition,it is established that sufficient and necessary conditions for Weyl's theorem for the functions of operators.