Geodesic
Kernels of Toeplitz operators on the Bergman space
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1119-1130
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A Coburn theorem says that a nonzero Toeplitz operator on the Hardy space is one-to-one or its adjoint operator is one-to-one. We study the corresponding problem for certain Toeplitz operators on the Bergman space.
A Coburn theorem says that a nonzero Toeplitz operator on the Hardy space is one-to-one or its adjoint operator is one-to-one. We study the corresponding problem for certain Toeplitz operators on the Bergman space.
DOI : 10.21136/CMJ.2023.0402-22
Classification : 32A36, 47B35
Keywords: Toeplitz operator; Bergman space 
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Lee, Young Joo. Kernels of Toeplitz operators on the Bergman space. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1119-1130. doi: 10.21136/CMJ.2023.0402-22

[1] Chen, Y., Izuchi, K. J., Lee, Y. J.: A Coburn type theorem on the Hardy space of the bidisk. J. Math. Anal. Appl. 466 (2018), 1043-1059. | DOI | MR | JFM

[2] Choe, B. R., Lee, Y. J.: Commuting Toeplitz operators on the harmonic Bergman space. Mich. Math. J. 46 (1999), 163-174. | DOI | MR | JFM

[3] Coburn, L. A.: Weyl's theorem for nonnormal operators. Mich. Math. J. 13 (1966), 285-288. | DOI | MR | JFM

[4] Guo, K., Zhao, X., Zheng, D.: The spectral picture of Bergman Toeplitz operators with harmonic polynomial symbols. Available at , 21 pages. | arXiv | MR

[5] Lee, Y. J.: A Coburn type theorem for Toeplitz operators on the Dirichlet space. J. Math. Anal. Appl. 414 (2014), 237-242. | DOI | MR | JFM

[6] McDonald, G., Sundberg, C.: Toeplitz operators on the disc. Indiana Univ. Math. J. 28 (1979), 595-611. | DOI | MR | JFM

[7] Perälä, A., Virtanen, J. A.: A note on the Fredholm properties of Toeplitz operators on weighted Bergman spaces with matrix-valued symbols. Oper. Matrices 5 (2011), 97-106. | DOI | MR | JFM

[8] Sundberg, C., Zheng, D.: The spectrum and essential spectrum of Toeplitz operators with harmonic symbols. Indiana Univ. Math. J. 59 (2010), 385-394. | DOI | MR | JFM

[9] Vukotić, D.: A note on the range of Toeplitz operators. Integr. Equations Oper. Theory 50 (2004), 565-567. | DOI | MR | JFM

[10] Zhu, K.: Operator Theory in Function Spaces. Mathematical Surveys and Monographs 138. AMS, Providence (2007). | DOI | MR | JFM

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