单位球上的对偶Toeplitz算子

Dual Toeplitz Operators on the Unit Ball

中文关键词:  对偶Toeplitz算子  单位球  紧性  谱  拟正规

英文关键词:Dual Toeplitz operators  unit ball  compactness  spectrum  quasinormal

中文摘要:

      本文研究了单位球Bergman空间的直交补上的对偶Toeplitz算子的代数性质,首先我们给出了对偶Toeplitz算子的有界性和紧性的完全刻画,然后给出对偶Toeplitz算子的谱性质,最后证明了不存在以有界全纯或者反全纯函数为符号的拟正规对偶Toeplitz算子.

英文摘要:

      In this paper, we study some properties of dual Toeplitz operators on the orthogonal complement of Bergman space of the unit ball. We first completely characterize the boundedness and compactness of dual Toeplitz operators. Then we obtain spectral properties of dual Toeplitz operators. Finally, we show that there are no quasinormal dual Toeplitz operators with bounded holomorphic or anti-holomorphic symbols.