谱距离与谱收敛

SPECTRAL DISTANCE AND SPECTRAL CONVERGENCE

研究了两个算子的谱及局部谱与它们的谱距离之间的关系:定理3 若L(X)序列完备,T_1,T_2∈L(X),T_1具有单值扩张性质,则d(σ(T_1),σ(T_2))≤ρ(T_1,T_2)定理4 若X序列完备,T_1,T_2,∈L(X),T_2具有单值扩张性质,则对任何x∈X,d(σ(T_1,x)σ(T_2,x))≤ρ(T_1,T_2)还利用以上结果讨论了谱收敛的一些性质.

It studied the relations between spectrum or local spectrum and spectral distance qf two linear continuous operators:Theorem 3 If L(X) is sequentially complete, T1,T2,L(X), T1 has the single valued extension property, thenTheorem 4 If X is sequentially complete, T1,T2L(X), T2 has the single valued extension property, then for every x X,It also used these results to discuss some properties of spectral convergence.