调和Dirichlet空间上的Toeplitz算子

夏锦, 王晓峰, 曹广福

数学学报 ›› 2013, Vol. 56 ›› Issue (3) : 311-330.

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PDF(574 KB)
数学学报 ›› 2013, Vol. 56 ›› Issue (3) : 311-330. DOI: 10.12386/A2013sxxb0032
论文

调和Dirichlet空间上的Toeplitz算子

    夏锦, 王晓峰, 曹广福
作者信息 +

Toeplitz Operators on Harmonic Dirichlet Space

    Jin XIA, Xiao Feng WANG, Guang Fu CAO
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文章历史 +

摘要

刻画了调和Dirichlet空间上Toeplitz算子的有界性、 紧性,讨论了Toeplitz算子的代数性质,得到了Toeplitz代数与Hankel代数的短正合列.还计算了Toeplitz代数与Hankel代数中Fredholm算子的Fredholm指标,得到了Toeplitz代数与Hankel代数的K0与K1群.

Abstract

We characterize the bounded ness and compact ness of the Toeplitz operators on the harmonic Dirichle space; discuss the algebraic properties of the Toeplitz operators; and obtain the short exact sequences with respect to the Toeplitz algebra and the Hankel algebra. We also compute the Fredholm index of Fredholm operator in the Toeplitz algebra and the Hankel algebra, and obtain the K0 and K1 groups of the Toeplitz algebra and the Hankel algebra.

关键词

调和Dirichlet空间 / Toeplitz算子 / Hankel算子

Key words

harmonic Dirichlet space / Toeplitz operator / Hankel operator

引用本文

导出引用
夏锦, 王晓峰, 曹广福. 调和Dirichlet空间上的Toeplitz算子. 数学学报, 2013, 56(3): 311-330 https://doi.org/10.12386/A2013sxxb0032
Jin XIA, Xiao Feng WANG, Guang Fu CAO. Toeplitz Operators on Harmonic Dirichlet Space. Acta Mathematica Sinica, Chinese Series, 2013, 56(3): 311-330 https://doi.org/10.12386/A2013sxxb0032

参考文献

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基金

国家自然科学基金资助项目(11271092)

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