加权Bergman空间上的紧算子

于涛;孙善利

数学学报 ›› 2001, Vol. 44 ›› Issue (2) : 233-240.

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PDF(384 KB)
数学学报 ›› 2001, Vol. 44 ›› Issue (2) : 233-240. DOI: 10.12386/A2001sxxb0032
论文

加权Bergman空间上的紧算子

    于涛;孙善利
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Compact Toeplitz Operators on the Weighted Bergman Spaces

    Tao YU,Shan Li SUN
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摘要

本文讨论了加权Bergman空间上的Toeplitz算子,证明了Toplitz算子的有限乘积的有限和是紧的当且仅当它的Berezin变换在边界上趋向于零.

Abstract

In this paper, we investigate the Toeplitz operators on the weighted Bergman spaces. It is shown that if S is the finite sum of finite product of Toeplitz operators, then S is compact iff the Berezin transform of S vanishes at the boundary of the unit disk.

关键词

Berezin变换 / 加权Bergman空间 / Toeplitz算子

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于涛;孙善利. 加权Bergman空间上的紧算子. 数学学报, 2001, 44(2): 233-240 https://doi.org/10.12386/A2001sxxb0032
Tao YU,Shan Li SUN. Compact Toeplitz Operators on the Weighted Bergman Spaces. Acta Mathematica Sinica, Chinese Series, 2001, 44(2): 233-240 https://doi.org/10.12386/A2001sxxb0032
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