加权Bergman空间上一类斜Toeplitz算子的交换性
Commutativity of a Class of Slant Toeplitz Operators on the Weighted Bergman Space
DOI: 10.12677/PM.2022.1210183, PDF,    科研立项经费支持
作者: 刘朝美, 张文婷, 蒋志娟：大连交通大学理学院，辽宁 大连
关键词: 加权Bergman空间；斜Toeplitz算子；交换性；Weighted Bergman Space； Slant Toeplitz Operator； Commutativity
摘要: 本文研究了单位圆盘的加权Bergman空间上斜Toeplitz算子的交换性，得到了两个带有解析符号的斜Toeplitz算子可交换的充要条件是它们的符号函数是线性相关的，以特殊单项式函数为符号的斜Toeplitz算子与带有解析符号的斜Toeplitz算子可交换的充要条件。
Abstract: In this paper, we study the commutativity of slant Toeplitz operators on the weighted Bergman space of the unit disk, and obtain the necessary and sufficient condition for the commutativity of two Toeplitz operators with analytic symbols which is that their symbol functions are linearly de-pendent, and the necessary and sufficient conditions for slant Toeplitz operators with special monomial symbols that commute with slant Toeplitz operators with analytic symbols.
文章引用：刘朝美, 张文婷, 蒋志娟. 加权Bergman空间上一类斜Toeplitz算子的交换性[J]. 理论数学, 2022, 12(10): 1693-1701. https://doi.org/10.12677/PM.2022.1210183

参考文献

[1] Ho, M.C. (1996) Properties of Slant Toeplitz Operators. Indiana University Mathematics Journal, 45, 843-862. [Google Scholar] [CrossRef] 
[2] Ho, M.C. (1997) Spectra of Slant Toeplitz Operators with Con-tinuous Symbol. Michigan Mathematical Journal, 44, 157-166. [Google Scholar] [CrossRef] 
[3] Ho, M.C. (1997) Adjoints of Slant Toeplitz Operators. Integral Equations and Operator Theory, 29, 301-302. [Google Scholar] [CrossRef] 
[4] Ho, M.C. (2001) Adjoints of Slant Toeplitz Operators II. Integral Equations and Operator Theory, 41, 179-188. [Google Scholar] [CrossRef] 
[5] Arora, S.C. and Batra, R. (2003) On Generalized Slant Toeplitz Opera-tors. Indian Journal of Mathematics, 45, 121-134.
[6] Arora, S.C. and Batra, R. (2005) Generalized Slant Toeplitz Operators on H2. Mathematische Nachrichten, 278, 347-355. [Google Scholar] [CrossRef] 
[7] 安恒斌, 蹇人宜. Bergman空间上的斜Toeplitz算子[J]. 数学学报, 2004, 47(1): 103-110.
[8] Yang, J., Leng, A.P. and Lu, Y.F. (2007) k-Order Slant Toeplitz Operators on the Bergman Space. Northeastern Mathematical Journal, 23, 403-412.
[9] Lu, Y.F., Liu, C.M. and Yang, J. (2010) Commutativity of kth-Order Slant Toeplitz Operators. Mathematische Nachrichten, 283, 1304-1313. [Google Scholar] [CrossRef] 
[10] Liu, C.M. and Lu, Y.F. (2013) Product and Commutativity of kth-Order Slant Toeplitz Operators. Abstract and Applied Analysis, 45, 900-914.
[11] Zhu, K.H. (1990) Operator Theory in Function Spaces. M. Dekker, New York.

为你推荐