We characterize all the Toeplitz operators that are complex symmetric with respect to a class of conjugations induced by a permutation. Our results provide an affirmative answer to a conjecture from a paper of Chattopadhyay et al. (2023) [1].
A. Chattopadhyaya, S. Das, C. Pradhan and S. Sarkar: Characterization of C-symmetric Toeplitz operators for a class of conjugations in Hardy spaces, Linear Multilinear Algebra, 71 (2023), 2026–2048.
R. G. Douglas: Banach Algebra Techniques in Operator Theory, Graduate Texts in Mathematics, 2nd ed., Springer (1998).
M. T. Garayev, M. Gürdal: Remarks on the zero Toeplitz product problem in the Bergman and Hardy spaces, Turkish J. Math., 42 (2018), 1504–1508.
M. T. Garayev, M. Gürdal, S. Saltan and U. Yamancı: dist-formulas and Toeplitz operators, Ann. Funct. Anal., 6 (2015), 221–226.
S. R. Garcia, E. Prodan and M. Putinar: Mathematical and physical aspects of complex symmetric operators, J. Phys. A, 47 (2014), 54 pp.
S. R. Garcia, M. Putinar: Complex symmetric operators and applications, Trans. Amer. Math. Soc., 358 (2006), 1285–1315.
S. R. Garcia, M. Putinar: Complex symmetric operators and applications. II, Trans. Amer. Math. Soc., 359 (2007), 3913–3931.
S. R. Garcia, W. Wogen: Some new classes of complex symmetric operators, Trans. Amer. Math. Soc., 362 (2010), 6065–6077.
K. Guo, S. Zhu: A canonical decomposition of complex symmetric operators, J. Operator Theory, 72 (2014), 529–547.
M. Gürdal, F. Söhret: Some results for Toeplitz operators on the Bergman space, Appl. Math. Comput., 218 (2011), 789–793.
M. T. Karaev, M. Gürdal and U. Yamancı: Some results related with Berezin symbols and Toeplitz operators, Math. Inequal. Appl., 17 (2014), 1031–1045.
E. Ko and J. E. Lee: On complex symmetric Toeplitz operators, J. Math. Anal. Appl., 434 (2016), 20–34.
E. Ko, J. E. Lee and J. Lee: Conjugations and complex symmetric Toeplitz operators on the weighted Hardy space, Mediterr. J. Math., 18 (2021), Article ID: 125.
E. Ko, J. E. Lee and J. Lee: Complex symmetric Toeplitz operators on the weighted Bergman space, Complex Var. Elliptic Equ., 67 (2022), 1393–1408.
A. Li, Y. Liu and Y. Chen: Complex symmetric Toeplitz operators on the Dirichlet space, J. Math. Anal. Appl., 487 (2020), 123998.
R. Li, Y. Yang and Y. Lu: A class of complex symmetric Toeplitz operators on Hardy and Bergman spaces, J. Math. Anal. Appl., 489 (2020), 124173.
C. O. Lo, A.W. K. Loh: Complex symmetric Toeplitz operators on Hilbert spaces of analytic functions, Mediterr. J. Math., 20 (2023), Article ID: 175.
K. Zhu: Operator theory in function spaces, 2nd ed., Mathematical Surveys and Monographs, 138, Amer. Math. Soc., Providence (2007).
A. Chattopadhyaya, S. Das, C. Pradhan and S. Sarkar: Characterization of C-symmetric Toeplitz operators for a class of conjugations in Hardy spaces, Linear Multilinear Algebra, 71 (2023), 2026–2048.
R. G. Douglas: Banach Algebra Techniques in Operator Theory, Graduate Texts in Mathematics, 2nd ed., Springer (1998).
M. T. Garayev, M. Gürdal: Remarks on the zero Toeplitz product problem in the Bergman and Hardy spaces, Turkish J. Math., 42 (2018), 1504–1508.
M. T. Garayev, M. Gürdal, S. Saltan and U. Yamancı: dist-formulas and Toeplitz operators, Ann. Funct. Anal., 6 (2015), 221–226.
S. R. Garcia, E. Prodan and M. Putinar: Mathematical and physical aspects of complex symmetric operators, J. Phys. A, 47 (2014), 54 pp.
S. R. Garcia, M. Putinar: Complex symmetric operators and applications, Trans. Amer. Math. Soc., 358 (2006), 1285–1315.
S. R. Garcia, M. Putinar: Complex symmetric operators and applications. II, Trans. Amer. Math. Soc., 359 (2007), 3913–3931.
S. R. Garcia, W. Wogen: Some new classes of complex symmetric operators, Trans. Amer. Math. Soc., 362 (2010), 6065–6077.
K. Guo, S. Zhu: A canonical decomposition of complex symmetric operators, J. Operator Theory, 72 (2014), 529–547.
M. Gürdal, F. Söhret: Some results for Toeplitz operators on the Bergman space, Appl. Math. Comput., 218 (2011), 789–793.
M. T. Karaev, M. Gürdal and U. Yamancı: Some results related with Berezin symbols and Toeplitz operators, Math. Inequal. Appl., 17 (2014), 1031–1045.
E. Ko and J. E. Lee: On complex symmetric Toeplitz operators, J. Math. Anal. Appl., 434 (2016), 20–34.
E. Ko, J. E. Lee and J. Lee: Conjugations and complex symmetric Toeplitz operators on the weighted Hardy space, Mediterr. J. Math., 18 (2021), Article ID: 125.
E. Ko, J. E. Lee and J. Lee: Complex symmetric Toeplitz operators on the weighted Bergman space, Complex Var. Elliptic Equ., 67 (2022), 1393–1408.
A. Li, Y. Liu and Y. Chen: Complex symmetric Toeplitz operators on the Dirichlet space, J. Math. Anal. Appl., 487 (2020), 123998.
R. Li, Y. Yang and Y. Lu: A class of complex symmetric Toeplitz operators on Hardy and Bergman spaces, J. Math. Anal. Appl., 489 (2020), 124173.
C. O. Lo, A.W. K. Loh: Complex symmetric Toeplitz operators on Hilbert spaces of analytic functions, Mediterr. J. Math., 20 (2023), Article ID: 175.
K. Zhu: Operator theory in function spaces, 2nd ed., Mathematical Surveys and Monographs, 138, Amer. Math. Soc., Providence (2007).
Lo, C. O., & Loh, A. W. K. (2024). C-symmetric Toeplitz operators on Hardy spaces. Constructive Mathematical Analysis, 7(3), 126-133. https://doi.org/10.33205/cma.1503726
AMA
Lo CO, Loh AWK. C-symmetric Toeplitz operators on Hardy spaces. CMA. September 2024;7(3):126-133. doi:10.33205/cma.1503726
Chicago
Lo, Ching On, and Anthony Wai Keung Loh. “C-Symmetric Toeplitz Operators on Hardy Spaces”. Constructive Mathematical Analysis 7, no. 3 (September 2024): 126-33. https://doi.org/10.33205/cma.1503726.
EndNote
Lo CO, Loh AWK (September 1, 2024) C-symmetric Toeplitz operators on Hardy spaces. Constructive Mathematical Analysis 7 3 126–133.
IEEE
C. O. Lo and A. W. K. Loh, “C-symmetric Toeplitz operators on Hardy spaces”, CMA, vol. 7, no. 3, pp. 126–133, 2024, doi: 10.33205/cma.1503726.
ISNAD
Lo, Ching On - Loh, Anthony Wai Keung. “C-Symmetric Toeplitz Operators on Hardy Spaces”. Constructive Mathematical Analysis 7/3 (September 2024), 126-133. https://doi.org/10.33205/cma.1503726.
JAMA
Lo CO, Loh AWK. C-symmetric Toeplitz operators on Hardy spaces. CMA. 2024;7:126–133.
MLA
Lo, Ching On and Anthony Wai Keung Loh. “C-Symmetric Toeplitz Operators on Hardy Spaces”. Constructive Mathematical Analysis, vol. 7, no. 3, 2024, pp. 126-33, doi:10.33205/cma.1503726.
Vancouver
Lo CO, Loh AWK. C-symmetric Toeplitz operators on Hardy spaces. CMA. 2024;7(3):126-33.