Abstract
In this paper semicommutators of truncated Toeplitz operators on some model space are discussed. We investigate when the product or the semicommutator of two truncated Toeplitz operators is zero, respectively. We also obtain a necessary and sufficient condition for the semicommutator of two truncated Toeplitz operators to be compact.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
No datasets were generated or analysed during the current study.
References
Axler, S., Chang, S.-Y., Sarason, D.: Product of Toeplitz operators. Intergral Equ. Oper. Theory 1, 285–309 (1978)
Chu, C.: Product of truncated Hankel and truncated Toeplitz operators. J. Math. Anal. Appl. 489, 124–136 (2020)
Douglas, R.G.: Banach Algebra Techniques in the Operator Theory. Academic Press, New York (1972)
Gorkin, P., Zheng, D.: Essentially commuting Toeplitz operators. Pac. J. Math. 190, 87–109 (1999)
Guo, K., Zheng, D.: Essentially commuting Hankel and Toeplitz operators. J. Funct. Anal. 201, 121–147 (2003)
Ma, P., Zheng, D.: Compact truncated Toeplitz operators. J. Funct. Anal. 270, 4256–4279 (2016)
Sarason, D.: Algebraic properties of truncated Toeplitz operators. Oper. Matrices 1(4), 491–526 (2007)
Sedlock, N.A.: Algebras of truncated Toeplitz operators. Oper. Matrices 5(2), 309–326 (2011)
Volberg, A.L.: Two remarks concerning the theorem of S. Axler, S-Y. A. Chang, and D. Sarason. J. Oper. Theory 8, 209–218 (1982)
Acknowledgements
This work is partially supported by the NNSFC (Grant No. 11971087).
Author information
Authors and Affiliations
Contributions
All authors wrote the main manuscript text and reviewed the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no competing interests.
Additional information
Communicated by Javad Mashreghi.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhao, X., Yu, T. Semicommutators of Truncated Toeplitz Operators. Complex Anal. Oper. Theory 18, 96 (2024). https://doi.org/10.1007/s11785-024-01540-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11785-024-01540-2