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Dilation theory and analytic model theory for doubly commuting sequences of C·0-contractions

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Abstract

It is known that every C·0-contraction has a dilation to a Hardy shift. This leads to an elegant analytic functional model for C·0-contractions, and has motivated lots of further works on the model theory and generalizations to commuting tuples of C·0-contractions. In this paper, we focus on doubly commuting sequences of C·0-contractions, and establish the dilation theory and the analytic model theory for these sequences of operators. These results are applied to generalize the Beurling-Lax theorem and Jordan blocks in the multivariable operator theory to the operator theory in the infinite-variable setting.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11871157 and 12101428). The authors thank the referees for reading this paper in great detail, and providing helpful suggestions. The authors thank Professor Yi Wang for discussion on the proof of Proposition 4.2.

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Authors and Affiliations

  1. College of Mathematics, Sichuan University, Chengdu, 610065, China

    Hui Dan

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Kunyu Guo

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  1. Hui Dan
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  2. Kunyu Guo
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Correspondence to Kunyu Guo.

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Dan, H., Guo, K. Dilation theory and analytic model theory for doubly commuting sequences of C·0-contractions. Sci. China Math. 66, 303–340 (2023). https://doi.org/10.1007/s11425-020-1965-1

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  • DOI: https://doi.org/10.1007/s11425-020-1965-1

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