论文标题
磁盘伯格曼空间上的不正常的toeplitz操作员
Hyponormal Toeplitz Operators on the Bergman Space of the Disk
论文作者
论文摘要
我们考虑具有作用在设备磁盘的伯格曼空间并评估其不正常状态的有限符号的Toeplitz操作员。我们将主要关注符号$φ（z）= z^{n} | z | |^{2S}+a（t）\ bar {z}^{m} | z | |^{2t} $，其中$ s $和$ s $和$ t $是正数，$ m $和$ m $和$ n $是天然号码。主要目标是了解该操作员的大小$ | a（t）| $是不正常的，我们将以$ t $的大价值回答这个问题。我们还从2019年的Fleman和Liaw论文中纠正了有关Toeplitz操作员的委托书的标准$ z^m \ bar {z}^n $时的错别字。
We consider Toeplitz operators with bounded symbol acting on the Bergman space of the unit disk and assess their hyponormality. We will mainly be concerned with the symbol $φ(z)=z^{n}|z|^{2s}+a(t)\bar{z}^{m}|z|^{2t}$, where $s$ and $t$ are positive real numbers and $m$ and $n$ are natural numbers. The main goal is to understand how large $|a(t)|$ can be for this operator to be hyponormal and we will answer this question for large values of $t$. We also correct a typo from a 2019 paper of Fleeman and Liaw concerning the norm of the commutator of the Toeplitz operator with symbol $z^m\bar{z}^n$ when $m>n$.
