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C-symmetric Toeplitz operators on Hardy spaces

Yıl 2024, , 126 - 133, 15.09.2024
https://doi.org/10.33205/cma.1503726

Öz

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].

Kaynakça

  • 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).
Yıl 2024, , 126 - 133, 15.09.2024
https://doi.org/10.33205/cma.1503726

Öz

Kaynakça

  • 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).
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Operatör Cebirleri ve Fonksiyonel Analiz
Bölüm Makaleler
Yazarlar

Ching On Lo 0000-0003-2735-8726

Anthony Wai Keung Loh Bu kişi benim 0000-0002-2759-3198

Erken Görünüm Tarihi 27 Ağustos 2024
Yayımlanma Tarihi 15 Eylül 2024
Gönderilme Tarihi 23 Haziran 2024
Kabul Tarihi 22 Ağustos 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

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. Eylül 2024;7(3):126-133. doi:10.33205/cma.1503726
Chicago Lo, Ching On, ve Anthony Wai Keung Loh. “C-Symmetric Toeplitz Operators on Hardy Spaces”. Constructive Mathematical Analysis 7, sy. 3 (Eylül 2024): 126-33. https://doi.org/10.33205/cma.1503726.
EndNote Lo CO, Loh AWK (01 Eylül 2024) C-symmetric Toeplitz operators on Hardy spaces. Constructive Mathematical Analysis 7 3 126–133.
IEEE C. O. Lo ve A. W. K. Loh, “C-symmetric Toeplitz operators on Hardy spaces”, CMA, c. 7, sy. 3, ss. 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 (Eylül 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 ve Anthony Wai Keung Loh. “C-Symmetric Toeplitz Operators on Hardy Spaces”. Constructive Mathematical Analysis, c. 7, sy. 3, 2024, ss. 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.