We consider an approximation problem related to strongly irreducible operators,that is,does the direct sum of a strongly irreducible operator inβ_∞(Ω) and certain operator have a small compact perturbation which is a strongly irreducible operator inβ_∞(Ω)? In this paper,we prove that the direct sum of any strongly irreducible operator inβ_∞(Ω) and certain biquasitriangular operator have small compact perturbations which are strongly irreducible operators inβ_∞(Ω).
二操作员 A, B ∈
ℬ
(ℋ
) 被说是强烈近似地类似,由 A∼ sas B 给 ɛ
>
的(i) 0,在那里存在 K i ∈有 ∥K i ∥<
ɛ
(i = 1, 2 ) 以便 + K 1 和 B + K 2 是类似的;(i i )σ
0(A)=σ
0(B) 和暗淡 ℋ
(λ;一)= 暗淡 ℋ
( λ;B ) 为每 λ
∈
σ
0(A) 。在这篇论文,我们证明下列结果。让 S, T ∈
ℬ
(ℋ
) 是伪三角形令人满意:(i)σ
(T)=σ
(S)=σ
w (S) 被连接并且 σ
e (S)=σ
lre (S) ;(i i )ρ
s-F (S)∩
σ
(S) 由至多有限的部件组成,每部件 Ω
满足那 Ω
= int,在 int 是内部的地方。那么, S ∼
sas T 如果并且仅当 S 和 T 是实质上类似的。