算子函数的Weyl定理及其稳定性

Weyl’s Theorem for Functions of Operators and Stability

设H是无限维复Hilbert空间,B(H)表示H上的有界线性算子全体构成的集合.本文对B(H)中使得f(T)满足Weyl定理的算子进行刻画,其中f是T的谱集的某个邻域上的解析函数.同时,也对算子函数的Weyl定理及算子Weyl定理的摄动之间的关系进行了讨论.

Let H be a complex infinite dimensional Hilbert space.B(H)denotes the algebra of all bounded linear operators on H.In this paper,we characterize the operators in B(H)for which f(T)satisfies Weyl’s theorem,where f denotes the analytic function on some neighbourhood of the spectrum of T.Also,the relationships between Weyl’s theorem for functions of operators and the stability of Weyl’s theorem are explored.