Abstract
In this paper, we introduce a new conjugation induced by a sequence of symmetric unitary n × n matrices on ℂn. And we completely characterize the complex symmetric composition operator Cϕ on the Hardy space of the unit ball with respect to the conjugation mentioned above. Furthermore, we propose an interesting open question under the background of this problem: whether every square complex matrix is symmetrically unitarily equivalent to its transpose (SUET).
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Acknowledgements
The work was supported in part by the National Natural Science Foundation of China (Nos. 12271396, 12171353).
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Dong, X., Guo, Y. & Zhou, Z. Complex Symmetric Composition Operators on the Hardy Space of the Unit Ball. Front. Math (2024). https://doi.org/10.1007/s11464-023-0040-y
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DOI: https://doi.org/10.1007/s11464-023-0040-y