Abstract
Let T be a rooted, countable infinite tree without terminal vertices. In the present paper, we investigate the spectra, self-adjointness, positivity, compactness, and Schatten class membership of Toeplitz operators on the spaces of p-summable functions on T. Moreover, we obtain a necessary and sufficient condition for Toeplitz operators to have finite rank on such function spaces.
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Acknowledgements
The authors would like to thank the reviewer for the constructive and valuable comments and suggestions. This work was partially supported by NSFC (Grant No. 12371125) and Chongqing Natural Science Foundation (cstc2019jcyj-msxmX0337). The third author was partially supported by the Fundamental Research Funds for the Central Universities (Grant Nos. 2020CDJQY-A039, 2020CDJ-LHSS-003).
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Huang, M., Zhang, X. & Zhao, X. Toeplitz Operators on \({\mathcal {L}}^p\)-Spaces of a Tree. Mediterr. J. Math. 20, 321 (2023). https://doi.org/10.1007/s00009-023-02526-8
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DOI: https://doi.org/10.1007/s00009-023-02526-8