Characterizations of the product of asymmetric dual truncated Toeplitz operators

Zhenhui Zhu; Qi Wu; Yong Chen; Zhenhui Zhu; Qi Wu; Yong Chen

doi:10.3934/math.2025300

AIMS Mathematics

2025, Volume 10, Issue 3: 6560-6573. doi: 10.3934/math.2025300

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Characterizations of the product of asymmetric dual truncated Toeplitz operators

Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China

Received: 06 December 2024 Revised: 08 March 2025 Accepted: 19 March 2025 Published: 25 March 2025
MSC : Primary 47B35, Secondary 32A37

The asymmetric dual truncated Toeplitz operator (ADTTO) is a compression multiplication operator acting on the orthogonal complement of two different model spaces. In this paper, we present an operator equation characterization of an ADTTO using the compressed shift operator. As an application, the product of two ADTTOs with certain symbols being another ADTTO is obtained.
- asymmetric dual truncated Toeplitz operator,
- Hardy space,
- model space,
- product problem
Citation: Zhenhui Zhu, Qi Wu, Yong Chen. Characterizations of the product of asymmetric dual truncated Toeplitz operators[J]. AIMS Mathematics, 2025, 10(3): 6560-6573. doi: 10.3934/math.2025300

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Abstract

The asymmetric dual truncated Toeplitz operator (ADTTO) is a compression multiplication operator acting on the orthogonal complement of two different model spaces. In this paper, we present an operator equation characterization of an ADTTO using the compressed shift operator. As an application, the product of two ADTTOs with certain symbols being another ADTTO is obtained.

References

[1]	A. Brown, P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math., 213 (1964), 89–102. https://doi.org/10.1515/crll.1964.213.89 doi: 10.1515/crll.1964.213.89
[2]	M. C. Câmara, K. Kliś-Garlicka, M. Ptak, (Asymmetric) dual truncated Toeplitz operators, In: R. M. Aron, M. S. Moslehian, I. M. Spitkovsky, H. J. Woerdeman, Operator and norm inequalities and related topics, Trends in Mathematics, Birkhäuser/Springer, Cham, 2022,429–460. https://doi.org/10.1007/978-3-031-02104-6_13
[3]	X. H. Ding, Y. Q. Sang, Dual truncated Toeplitz operators, J. Math. Anal. Appl., 461 (2018), 929–946. https://doi.org/10.1016/j.jmaa.2017.12.032 doi: 10.1016/j.jmaa.2017.12.032
[4]	S. R. Garcia, J. E. Mashreghi, W. Ross, Introduction to model spaces and their operators, Cambridge University Press, 2016. https://doi.org/10.1017/CBO9781316258231
[5]	S. R. Garcia, M. Putinar, Complex symmetric operators and applications, Trans. Amer. Math. Soc., 358 (2006), 1285–1315.
[6]	C. Gu, Characterizations of dual truncated Toeplitz operators, J. Math. Anal. Appl., 496 (2021), 124815. https://doi.org/10.1016/j.jmaa.2020.124815 doi: 10.1016/j.jmaa.2020.124815
[7]	D. Sarason, Algebraic properties of truncated Toeplitz operators, Oper. Matrices, 1 (2007), 491–526. https://doi.org/10.7153/OAM-01-29 doi: 10.7153/OAM-01-29
[8]	N. Sedlock, Algebras of truncated Toeplitz operators, Oper. Matrices, 5 (2011), 309–326. https://doi.org/10.7153/oam-05-22 doi: 10.7153/oam-05-22

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