|
|
Bergman空间上Toeplitz算子的拟正规性和双正规性
|
Abstract:
本文主要研究Bergman空间上以非调和函数为符号的Toeplitz算子的拟正规性和双正规性：1) 以![\"\"](\"Edit_063ee268-490a-44e1-a4f1-11c92fab059d.png\")
为符号的Toeplitz算子的拟正规性和双正规性；2) 以![\"\"](\"Edit_6fda4411-1ab5-4050-bc03-d404332d88b1.png\")
为符号的Toeplitz算子的拟正规性和双正规性。
In this paper, we mainly study the quasi-normality and binormality of Toeplitz operators in Bergman space with non-harmonic functions: 1) The quasi-normality and binormality of Toeplitz operators with ![\"\"](\"Edit_f1bf8aa3-3b1f-44f8-9020-3c3e71a6406a.png\")
as symbols; 2) Quasi-normality and binormality of Toeplitz operators with ![\"\"](\"Edit_ea7f09d9-da28-409f-99c5-c3a245b28cd3.png\")
as symbols.
| [1] | Gu, C., Kang, D.O., Ko, E., et al. (2019) Binormal Toeplitz Operators on the Hardy Space. International Journal of Mathematics, 30, 1950001. https://doi.org/10.1142/S0129167X19500010 |
| [2] | Park, J.D. (2006) Bounded Toeplitz Products on the Bergman Space of the Unit Ball. Integral Equations and Operator Theory, 54, 571-584. https://doi.org/10.1007/s00020-005-1405-1 |
| [3] | Raimondo, R. (2000) Toeplitz Operators on the Bergman Space of the Unit Ball. Bulletin of the Australian Mathematical Society, 62, 273-285. https://doi.org/10.1017/S0004972700018748 |
| [4] | Ahern, P. and ？u？kovi？, ？. (2001) Products of Toeplitz Operators on the Bergman Space. Illinois Journal of Mathematics, 45, 113-121. https://doi.org/10.1215/ijm/1258138257 |
| [5] | Gu, C. and Kang, D. (2014) Normal Toeplitz and Hankel Operators with Operator-Valued Symbols. Houston Journal of Mathematics, 40, 1155-1181. |
| [6] | Faour, N. (1989) On Quasinormal, Subnormal, and Hyponormal Toeplitz Operators. Rendiconti del Circolo Matematico di Palermo, 38, 121-129. https://doi.org/10.1007/BF02844854 |
| [7] | Guediri, H. (2010) Quasinormality and Numerical Ranges of Certain Classes of Dual Toeplitz Operators. Abstract and Applied Analysis, 2010, Article ID 426319. https://doi.org/10.1155/2010/426319 |
| [8] | Kim, S. and Lee, J. (2020) Normal Toeplitz Operators on the Bergman Space. Mathematics, 8, 1463.
https://doi.org/10.3390/math8091463 |
| [9] | Simanek, B. (2019) Hyponormal Toeplitz Operators with Non-Harmonic Algebraic Symbol. Analysis and Mathematical Physics, 9, 1613-1626. https://doi.org/10.1007/s13324-018-00279-2 |
