Dirichlet空间上的Bergman型Toeplitz算子

黄穗, 何艳

数学学报 ›› 2013, Vol. 56 ›› Issue (6) : 951-956.

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数学学报 ›› 2013, Vol. 56 ›› Issue (6) : 951-956. DOI: 10.12386/A2013sxxb0091
论文

Dirichlet空间上的Bergman型Toeplitz算子

    黄穗1, 何艳2
作者信息 +

The Bergman-Type Toeplitz Operators on Dirichlet Space

    Sui HUANG1, Yan HE2
Author information +
文章历史 +

摘要

证明了在Dirichlet空间上以有界调和函数φ为符号的Bergman-型Toeplitz算子Tφ是紧算子的充分必要条件是其符号φ为0;如果φ是单位圆盘D上的连续函数,那么Tφ是紧算子的充分必要条件是φ在D的边界上为0.我们还讨论了此类Toeplitz算子的半换位子.

Abstract

We prove that a Bergman-type Toeplitz operator on Dirichlet space arising from a bounded and harmornic function is compact if and only if its symbol is zero. Moreover, if symbol is continue on D, then the Toeplitz operator is compact if and only if its symbol is vanished on boundary of D.

关键词

Dirichlet空间 / Bergman-型Toeplitz算子 / 紧算子

Key words

Dirichlet space / Bergman-type Toeplitz operator / compact operator

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黄穗, 何艳. Dirichlet空间上的Bergman型Toeplitz算子. 数学学报, 2013, 56(6): 951-956 https://doi.org/10.12386/A2013sxxb0091
Sui HUANG, Yan HE. The Bergman-Type Toeplitz Operators on Dirichlet Space. Acta Mathematica Sinica, Chinese Series, 2013, 56(6): 951-956 https://doi.org/10.12386/A2013sxxb0091

参考文献

[1] Axler S., Zheng D., Compact operators via the Berezin transform, Indiana Univ. Math. J., 1998, 47: 387-399.

[2] Cao G., Fredholm properties of Toeplitz operators on Dirichlet space, Pacific J. Math., 1999, 188: 209-223.

[3] Chartrand R., Toeplitz operators on the Dirichlet-type space, J. Oper. Theory, 2002, 48: 3-13.

[4] Douglas R. G., Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972.

[5] Yu T., Toeplitz operators on the Dirichlet space, Integr. Equ. Oper. Theory, 2010, 67: 163-170.

[6] Zhu K. H., Operator Theory in Function Space, Marcel Dekker, New York, 1990.

基金

国家自然科学基金(11271390);数学天元基金(11126349);重庆市教委科研项目(KJ130623)

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