For any given symmetric measure on the closed unit disk ■,we apply the Berezin transform to characterizing semi-commuting and commuting Toeplitz operators with bounded harmonic symbols on A2(■,d).
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。
