DOI QR코드

DOI QR Code

TOEPLITZ-TYPE OPERATORS ON THE FOCK SPACE F2α

  • Chunxu Xu (School of Mathematics and Information Science Guangzhou University) ;
  • Tao Yu (School of Mathematical Sciences Dalian University of Technology)
  • 투고 : 2022.06.20
  • 심사 : 2023.02.10
  • 발행 : 2023.07.31

초록

Let j be a nonnegative integer. We define the Toeplitz-type operators T(j)a with symbol a ∈ L(C), which are variants of the traditional Toeplitz operators obtained for j = 0. In this paper, we study the boundedness of these operators and characterize their compactness in terms of its Berezin transform.

키워드

과제정보

The authors are very grateful to the referee for his (or her) helpful suggestions and comments.

참고문헌

  1. L. Abreu and N. J. Faustino, On Toeplitz operators and localization operators, Proc. Amer. Math. Soc. 143 (2015), no. 10, 4317-4323. https://doi.org/10.1090/proc/12211 
  2. S. Axler and D. Zheng, Compact operators via the Berezin transform, Indiana Univ. Math. J. 47 (1998), no. 2, 387-400. https://doi.org/10.1512/iumj.1998.47.1407 
  3. W. Bauer and J. B. Isralowitz, Compactness characterization of operators in the Toeplitz algebra of the Fock space Fpα, J. Funct. Anal. 263 (2012), no. 5, 1323-1355. https://doi.org/10.1016/j.jfa.2012.04.020 
  4. L. A. Coburn, The Bargmann isometry and Gabor-Daubechies wavelet localization operators, in Systems, approximation, singular integral operators, and related topics (Bordeaux, 2000), 169-178, Oper. Theory Adv. Appl., 129, Birkhauser, Basel, 2001. 
  5. L. A. Coburn, J. B. Isralowitz, and B. Li, Toeplitz operators with BMO symbols on the Segal-Bargmann space, Trans. Amer. Math. Soc. 363 (2011), no. 6, 3015-3030. https://doi.org/10.1090/S0002-9947-2011-05278-5 
  6. E. Cordero and K. Grochenig, Time-frequency analysis of localization operators, J. Funct. Anal. 205 (2003), no. 1, 107-131. https://doi.org/10.1016/S0022-1236(03)00166-6 
  7. I. C. Daubechies, Time-frequency localization operators: a geometric phase space approach, IEEE Trans. Inform. Theory 34 (1988), no. 4, 605-612. https://doi.org/10.1109/18.9761 
  8. M. Englis, Toeplitz operators and group representations, J. Fourier Anal. Appl. 13 (2007), no. 3, 243-265. https://doi.org/10.1007/s00041-006-6009-x 
  9. M. Englis, Toeplitz operators and localization operators, Trans. Amer. Math. Soc. 361 (2009), no. 2, 1039-1052. https://doi.org/10.1090/S0002-9947-08-04547-9 
  10. H. G. Feichtinger and K. Nowak, A Szeg˝o-type theorem for Gabor-Toeplitz localization operators, Michigan Math. J. 49 (2001), no. 1, 13-21. https://doi.org/10.1307/mmj/1008719032 
  11. M.-L. Lo, The Bargmann transform and windowed Fourier localization, Integr. Equ. Oper. Theory 57 (2007), no. 3, 397-412. https://doi.org/10.1007/s00020-006-1462-0 
  12. D. H. Luecking, Trace ideal criteria for Toeplitz operators, J. Funct. Anal. 73 (1987), no. 2, 345-368. https://doi.org/10.1016/0022-1236(87)90072-3 
  13. D. Suarez, A generalization of Toeplitz operators on the Bergman space, J. Operator Theory 73 (2015), no. 2, 315-332. https://doi.org/10.7900/jot.2013nov28.2023 
  14. X. F. Wang, G. F. Cao, and K. Zhu, Boundedness and compactness of operators on the Fock space, Integr. Equ. Oper. Theory 77 (2013), no. 3, 355-370. https://doi.org/10.1007/s00020-013-2066-0 
  15. K. Zhu, Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains, J. Operator Theory 20 (1988), no. 2, 329-357.  https://doi.org/10.1016/0022-1236(88)90100-0
  16. K. Zhu, Operator theory in function spaces, second edition, Mathematical Surveys and Monographs, 138, Amer. Math. Soc., Providence, RI, 2007. https://doi.org/10.1090/surv/138 
  17. K. Zhu, Analysis on Fock spaces, Graduate Texts in Mathematics, 263, Springer, New York, 2012. https://doi.org/10.1007/978-1-4419-8801-0