Toeplitz algebra and spectra of Toeplitz operators on the harmonic Dirichlet space
Toeplitz algebra and spectra of Toeplitz operators on the harmonic Dirichlet space
复制标题
调和狄利克雷空间上的托普利茨代数和托普利茨算子谱
DOI：
10.1007/s43037-019-00037-x
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发表时间：
2020
影响因子：
1.2
通讯作者：
Zhao Xianfeng
中科院分区：
文献类型：
--
作者：
Luo Shuaibing;Zhao Xianfeng
本文研究调和Dirichlet空间上Toeplitz算子的代数性质和谱性质。我们完全刻画了这种函数空间上的Toeplitz代数和Hankel代数。利用代数曲线理论中的一些技巧，研究了具有解析多项式符号的Toeplitz算子的谱，证明了具有小于4次多项式符号的Toeplitz算子的谱等于一条闭曲线和至多100个孤立点的并.
In this paper, we study the algebraic and spectral properties of Toeplitz operators on the harmonic Dirichlet space. We completely characterize the Toeplitz algebra and Hankel algebra on such function space. Moreover, using some techniques in algebraic curves theory, we investigate the spectra of Toeplitz operators with analytic polynomial symbols and show that the spectrum of the Toeplitz operatorwithpa polynomial of degree less than 4 is equal to the union of a closed curve and at most finitely many isolated points.