论文标题
在加权伯格曼空间上
Hyponormal Toeplitz Operators on Weighted Bergman Spaces
论文作者
论文摘要
我们考虑在希尔伯特空间上作用的操作员，该操作员可以将其写入换档和对角线操作员的总和，并确定何时操作员何时是不正常的。条件是根据明确块雅各比矩阵的规范提出的。我们将此结果应用于Toeplitz运算符，其具有特定的代数符号，该符号作用于单位磁盘的某些加权伯格曼空间，并确定该操作员何时不符合不良状态。
We consider operators acting on a Hilbert space that can be written as the sum of a shift and a diagonal operator and determine when the operator is hyponormal. The condition is presented in terms of the norm of an explicit block Jacobi matrix. We apply this result to the Toeplitz operator with specific algebraic symbols acting on certain weighted Bergman spaces of the unit disk and determine when such operators are hyponormal.
