Positivity of Toeplitz operators via Berezin transform
Positivity of Toeplitz operators via Berezin transform
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DOI：
10.1016/j.jmaa.2014.03.020
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发表时间：
2014-08
影响因子：
1.3
通讯作者：
Xianfeng Zhao;Dechao Zheng
中科院分区：
文献类型：
--
作者：
Xianfeng Zhao;Dechao Zheng
本文通过Bergman空间上的正Toeplitz算子的Berezin变换，研究了其性质。令人惊讶的是，我们证明了Bergman空间上Toeplitz算子的正性并不完全由其符号的Berezin变换的正性决定。事实上，我们证明了，即使单位圆盘上的二次多项式的Berezin变换的最小值是正的，以函数为符号的Toeplitz算子也可能不是正的。
In this paper, we study positive Toeplitz operators on the Bergman space via their Berezin transforms. Surprisingly we show that the positivity of a Toeplitz operator on the Bergman space is not completely determined by the positivity of the Berezin transform of its symbol. In fact, we show that even if the minimal value of the Berezin transform of a quadratic polynomial of| z| on the unit disk is positive, the Toeplitz operator with the function as the symbol may not be positive.