Positivity of Fock Toeplitz Operators via the Berezin Transform

Citation:

Xianfeng ZHAO.Positivity of Fock Toeplitz Operators via the Berezin Transform[J].Chinese Annals of Mathematics B,2016,37(4):533~542
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Authors:

Xianfeng ZHAO;

Foundation:

This work was supported by the Chongqing Natural Science Foundation of China (No.cstc 2013jjB0050).
Abstract: This paper deals with the relationship between the positivity of the Fock Toeplitz operators and their Berezin transforms. The author considers the special case of the bounded radial function $\varphi(z)=a+b\rme^{-\alpha|z|^2}+c\rme^{-\beta|z|^2}$, where $a, b, c$ are real numbers and $\alpha, \beta$ are positive numbers. For this type of $\varphi$, one can choose these parameters such that the Berezin transform of $\varphi$ is a nonnegative function on the complex plane, but the corresponding Toeplitz operator $T_\varphi$ is not positive on the Fock space.

Keywords:

Positive Toeplitz operators, Fock space, Berezin transform

Classification:

47B35, 47B65
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