《一条摄动定理》一文的补遗

In this paper, a simple proof of the following perturbation theorem is given:Suppose that i) T is a self-adjoint operator in the Hilbert space with discrete spectrum σ(T)={λ_n|n=1,2,…}, λ_1≤λ_2≤… and λ_n=cn~P(1+0(1/n)),c>0, p>0.ii) Let 0≤v<1. Let P be a linear operator such that thedomain of P contains the domain of T~v and PT~(-v) is bounded.iii) p(1-v)>1.Then T+P has Property S and T+P and T have an asymptotically common decomposition. Furthermore, if v≤1/2, T+P has the strong Property S.