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| Positivity of Fock Toeplitz Operators via the Berezin Transform |
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Citation： |
Xianfeng ZHAO.Positivity of Fock Toeplitz Operators via the Berezin Transform[J].Chinese Annals of Mathematics B,2016,37(4):533~542 |
| Page view： 1779
Net amount： 1363 |
Authors： |
Xianfeng ZHAO; |
Foundation： |
This work was supported by the Chongqing Natural Science
Foundation of China (No.cstc 2013jjB0050). |
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| 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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