Let Ω be the unit ball or the polydisk of Cnand L2a(Ω) the Bergman space. In this paper we prove that if S is a finite sum of finite products of Toeplitz operators on L2a( Ω), then S is compact if and only if the B...Let Ω be the unit ball or the polydisk of Cnand L2a(Ω) the Bergman space. In this paper we prove that if S is a finite sum of finite products of Toeplitz operators on L2a( Ω), then S is compact if and only if the Berezin transform S(z) of S tends to zero as z→Ω.展开更多
The Sarason＇s Toeplitz product problem asks when the Toeplitz product operator TuTv, with analytic symbols u and v, is bounded on Hilbert space of analytic functions. In this paper, we deal with this problem on the F...The Sarason＇s Toeplitz product problem asks when the Toeplitz product operator TuTv, with analytic symbols u and v, is bounded on Hilbert space of analytic functions. In this paper, we deal with this problem on the Fock-Sobolev space and have a complete solution that u = eq, v = Ce-q, where q is a linear complex polynomial and C is a nonzero constant.展开更多
The aim of this work is to study the Berezin quantization of a Gaussian state. The result is another Gaussian state that depends on a quantum parameter α, which describes the relationship between the classical and qu...The aim of this work is to study the Berezin quantization of a Gaussian state. The result is another Gaussian state that depends on a quantum parameter α, which describes the relationship between the classical and quantum vision. The compression parameter λ>0 is associated to the harmonic oscillator semigroup.展开更多
In this paper we prove that the boundedness and compactness of Toeplitz operator with a BMOα1 symbol on the weighted Bergman space Aα2（Bn） of the unit ball is completely determined by the behavior of its Berezin t...In this paper we prove that the boundedness and compactness of Toeplitz operator with a BMOα1 symbol on the weighted Bergman space Aα2（Bn） of the unit ball is completely determined by the behavior of its Berezin transform, where ≥ -1 and n 〉 1.展开更多
In this paper, we study positive Toeplitz operators on the harmonic Bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the ...In this paper, we study positive Toeplitz operators on the harmonic Bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the Toeplitz operator is positive if and only if its Berezin transform is nonnegative on the disk. On the other hand, we construct a function such that the Toeplitz operator with this function as the symbol is not positive but its Berezin transform is positive on the disk. We also consider the harmonic Bergman space on the upper half plane and prove that in this case the positive Toeplitz operators with continuous integrable harmonic symbols must be the zero operator.展开更多
文摘Let Ω be the unit ball or the polydisk of Cnand L2a(Ω) the Bergman space. In this paper we prove that if S is a finite sum of finite products of Toeplitz operators on L2a( Ω), then S is compact if and only if the Berezin transform S(z) of S tends to zero as z→Ω.
基金Supported by National Natural Science Foundation of China(Grant Nos.11471084,11301101 and 11671152)Guangzhou Higher Education Science and Technology Pro ject(Grant No.2012A018)
文摘The Sarason＇s Toeplitz product problem asks when the Toeplitz product operator TuTv, with analytic symbols u and v, is bounded on Hilbert space of analytic functions. In this paper, we deal with this problem on the Fock-Sobolev space and have a complete solution that u = eq, v = Ce-q, where q is a linear complex polynomial and C is a nonzero constant.
文摘The aim of this work is to study the Berezin quantization of a Gaussian state. The result is another Gaussian state that depends on a quantum parameter α, which describes the relationship between the classical and quantum vision. The compression parameter λ>0 is associated to the harmonic oscillator semigroup.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10671028, 10971020）
文摘In this paper we prove that the boundedness and compactness of Toeplitz operator with a BMOα1 symbol on the weighted Bergman space Aα2（Bn） of the unit ball is completely determined by the behavior of its Berezin transform, where ≥ -1 and n 〉 1.
基金Supported by NSFC(Grant No.11271387)Chongqing Natural Sience Foundation(Grant No.cstc2013jjB0050)
文摘In this paper, we study positive Toeplitz operators on the harmonic Bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the Toeplitz operator is positive if and only if its Berezin transform is nonnegative on the disk. On the other hand, we construct a function such that the Toeplitz operator with this function as the symbol is not positive but its Berezin transform is positive on the disk. We also consider the harmonic Bergman space on the upper half plane and prove that in this case the positive Toeplitz operators with continuous integrable harmonic symbols must be the zero operator.
基金National Natural Science Foundation of China(11771139)National Natural Science Foundation of Zhejiang Province(LY20A010008)“Xinmiao”Projection for the undergraduate students of Zhejiang Province(2019R431003).
