摘要:
本文讨论了Bergman空间上两个形如T
fk，T
gk的Toeplitz算子，其中假设g
k=g
1(k)+g
2(k)，g
1(k)=
a
j(k) z
j，g
2(k)=
b
j(k)z
j∈H
∞(D)；f
k∈L
∞(D,dA)。f
k(re
iθ)=
f
p(k)(r)e
ipθ(1≤k≤N)。探究Toeplitz算子Tfk，Tgk的有限乘积有限和的相关问题，分析计算得到了其为零算子的一个必要条件。
Abstract:
This paper discusses two Toeplitz operators as T
fk, T
gk in Bergman space. In case g
k=g
1(k)+g
2(k), g
1(k)=
a
j(k) z
j, g
2(k)=
b
j(k)z
j∈H
∞(D); f
k∈L
∞(D,dA). f
k(re
iθ)=
f
p(k)(r)e
ipθ(1≤k≤N). This paper explores the related problems of the sum of the finite products of the two Toeplitz operators as Tfk, Tgk under a large amount of data and calculations. A necessary condition of zero operator is obtained (N).