论文标题
带有谐波多项式符号的伯格曼toeplitz操作员的光谱图片
The spectral picture of Bergman Toeplitz operators with harmonic polynomial symbols
论文作者
论文摘要
在本文中，结果表明，一些与Toeplitz运算符光谱有关的新现象在伯格曼空间上具有有界的谐波符号。一方面，我们证明了带有符号$ {\ bar {z}+p} $的Toeplitz运算符的光谱始终连接到每个多项式$ p $，学位小于$ 3 $。另一方面，我们表明，对于每个整数$ k $大于$ 2 $，都存在一个多项式$ p $ $ k $的$ k $，使得带有符号$ {\ bar {z}+p} $的Toeplitz Operator的频谱至少具有一个孤立的点，但最有一定的孤立点。然后将这些结果应用于获得新的非催眠型托管操作员，并在伯格曼定理保留的伯格曼空间上具有有界的谐波符号。
In this paper, it is shown that some new phenomenon related to the spectra of Toeplitz operators with bounded harmonic symbols on the Bergman space. On the one hand, we prove that the spectrum of the Toeplitz operator with symbol ${\bar{z}+p}$ is always connected for every polynomial $p$ with degree less than $3$. On the other hand, we show that for each integer $k$ greater than $2$, there exists a polynomial $p$ of degree $k$ such that the spectrum of the Toeplitz operator with symbol ${\bar{z}+p}$ has at least one isolated point but has at most finitely many isolated points. Then these results are applied to obtain a new class of non-hyponormal Toeplitz operators with bounded harmonic symbols on the Bergman space for which Weyl's theorem holds.
