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Year 2024, Volume: 7 Issue: 3, 126 - 133, 15.09.2024

Ching On Lo , Anthony Wai Keung Loh

https://doi.org/10.33205/cma.1503726

Abstract

References

  • 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).

C-symmetric Toeplitz operators on Hardy spaces

Year 2024, Volume: 7 Issue: 3, 126 - 133, 15.09.2024

Ching On Lo , Anthony Wai Keung Loh

https://doi.org/10.33205/cma.1503726

Abstract

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].

Keywords

Toeplitz operators conjugations complex symmetric Hardy spaces

References

  • 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).
There are 18 citations in total.

Details

Primary Language English
Subjects Operator Algebras and Functional Analysis
Journal Section Articles
Authors

Ching On Lo 0000-0003-2735-8726

Anthony Wai Keung Loh This is me 0000-0002-2759-3198

Early Pub Date August 27, 2024
Publication Date September 15, 2024
Submission Date June 23, 2024
Acceptance Date August 22, 2024
Published in Issue Year 2024 Volume: 7 Issue: 3

Cite

APA 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 (September2024), 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.
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