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The commutant and invariant subspaces for dual truncated Toeplitz operators

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Abstract

Dual truncated Toeplitz operators on the orthogonal complement of the model space \(K_u^2(=H^2 \ominus uH^2)\) with u nonconstant inner function are defined to be the compression of multiplication operators to the orthogonal complement of \(K_u^2\) in \(L^2\). In this paper, we give a complete characterization of the commutant of dual truncated Toeplitz operator \(D_z\), and we even obtain the commutant of all dual truncated Toeplitz operators with bounded analytic symbols. Moreover, we describe the nontrival invariant subspaces of \(D_z\).

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Acknowledgements

The authors thank the referees for constructive comments. The first author was partially supported by the Natural Science Foundation of Chongqing (cstc2020jcyj-msxmX0318)and the grant from Chongqing Technology and Business University (2053010). The third author was partially supported by NSFC (11871122), the Program for University Innovation Team of Chongqing (CXTDX201601026), the Natural Science Foundation of Chongqing (cstc2018jcyjAX0595) and the grant (CTBU ZDPTTD201909).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, People’s Republic of China

    Yongning Li & Xuanhao Ding

  2. Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing, 400067, People’s Republic of China

    Yongning Li & Xuanhao Ding

  3. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Yuanqi Sang

Authors
  1. Yongning Li
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  2. Yuanqi Sang
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  3. Xuanhao Ding
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Correspondence to Yuanqi Sang.

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Communicated by Christian Le Merdy.

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Li, Y., Sang, Y. & Ding, X. The commutant and invariant subspaces for dual truncated Toeplitz operators. Banach J. Math. Anal. 15, 17 (2021). https://doi.org/10.1007/s43037-020-00102-w

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  • DOI: https://doi.org/10.1007/s43037-020-00102-w

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