Hyponormal Toeplitz operators with non-harmonic Symbol acting on the Bergman space
Hyponormal Toeplitz operators with non-harmonic Symbol acting on the Bergman space
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DOI：
10.7153/oam-2019-13-04
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发表时间：
2017-07
影响因子：
0.5
通讯作者：
Matthew Fleeman;C. Liaw
中科院分区：
文献类型：
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作者：
Matthew Fleeman;C. Liaw
作用于伯格曼空间 $A^{2}(\mathbb{D})$（符号为 $\varphi$）的托普利茨算子由 $T_{\varphi}f=P(\varphi f)$ 给出，其中 $P$ 是从 $L^{2}(\mathbb{D})$ 到伯格曼空间的投影。我们介绍了作用于 $A^{2}(\mathbb{D})$ 的次正规 Toeplitz 算子的研究历史，并给出了当 $\varphi$ 是非调和多项式时的结果。我们首次研究了具有非解析符号的次正规算子的普特南不等式。特别注意由于允许符号类别的扩展而出现的异常低正常行为。
The Toeplitz operator acting on the Bergman space $A^{2}(\mathbb{D})$, with symbol $\varphi$ is given by $T_{\varphi}f=P(\varphi f)$, where $P$ is the projection from $L^{2}(\mathbb{D})$ onto the Bergman space. We present some history on the study of hyponormal Toeplitz operators acting on $A^{2}(\mathbb{D})$, as well as give results for when $\varphi$ is a non-harmonic polynomial. We include a first investigation of Putnam's inequality for hyponormal operators with non-analytic symbols. Particular attention is given to unusual hyponormality behavior that arises due to the extension of the class of allowed symbols.