Reducing subspaces of multiplication operators with the symbol alpha z(k) + beta w(l) on L-a(2)(D-2)
Reducing subspaces of multiplication operators with the symbol alpha z(k) + beta w(l) on L-a(2)(D-2)
复制标题
在 L-a(2)(D-2) 上用符号 alpha z(k) beta w(l) 约简乘法运算符的子空间
DOI：
10.1007/s11425-015-4973-9
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发表时间：
2015
影响因子：
1.4
通讯作者：
Huang HanSong
中科院分区：
文献类型：
--
作者：
Wang XuDi;Dan Hui;Huang HanSong
定义在函数空间上的乘法算子一直受到算子论和函数论专家的极大关注。其中一个问题就是研究它们的子空间的约化。单变量案例取得了丰硕的成果。然而，在多变量的情况下，几乎没有采取什么行动。在Bergman空间的背景下，讨论了由特殊多项式Sp定义的乘法算子MP，其中(z，w)=αzk+βw1，α，β∈ℂ.完全确定了Mpp的约化子空间。
Multiplication operators defined on function spaces have been receiving enormous attention from both operator-theoretic and function-theoretic experts. One of the problems is to study reducing subspaces of them. The one-variable case has obtained fruitful remarkable results. However, little has been done in the multi-variable case. Under the setting of the Bergman space, this paper addresses those multiplication operatorsMpdefined by special polynomialsp, wherep(z,w) =αzk+βwl,α, β∈ ℂ. Those reducing subspaces ofMpare completely determined.