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On Some Algebras of Truncated Hankel and Asymmetric Truncated Hankel Operators

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Abstract

In the last decade, a large amount of research has been concentrated on the operators living on the model space. Asymmetric truncated Toeplitz operators and asymmetric truncated Hankel operators are the natural generalization of truncated Toeplitz operators and truncated Hankel operators respectively. In this paper, we obtained the basic results concerning the product of these operators and in terms of product their connection with each other. In addition, when an inner function has a certain symmetric property, some algebraic properties of truncated Hankel operators are also discussed.

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Acknowledgements

The authors sincerely appreciate all the valuable comments and suggestions of the referee, which helped us to improve the quality of the manuscript. This research work is supported by the General Direction of Scientific Research and Technological Development (DGRSDT), Algeria.

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Authors and Affiliations

  1. Laboratoire de mathématiques pures et appliquées, Université de Amar Telidji, 03000, Laghouat, Algeria

    Ameur Yagoub

  2. Department of Mathematics, University of Kotli Azad Jammu & Kashmir, Kotli, Azad Jammu & Kashmir, 11100, Pakistan

    Muhammad Ahsan Khan

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  1. Ameur Yagoub
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  2. Muhammad Ahsan Khan
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All authors equally participated during the prepartion of this manuscript.

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Correspondence to Muhammad Ahsan Khan.

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Communicated by Javad Mashreghi.

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This article is part of the topical collection “Harmonic Analysis and Operator Theory” edited by H. Turgay Kaptanoglu, Andreas Seeger, Franz Luef and Serap Oztop

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Yagoub, A., Khan, M.A. On Some Algebras of Truncated Hankel and Asymmetric Truncated Hankel Operators. Complex Anal. Oper. Theory 17, 130 (2023). https://doi.org/10.1007/s11785-023-01439-4

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