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Submodules in Polydomains and Noncommutative Varieties

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Abstract

Tensor product of Fock spaces is analogous to the Hardy space over the unit polydisc. This plays an important role in the development of noncommutative operator theory and function theory in the sense of noncommutative polydomains and noncommutative varieties. In this paper we study joint invariant subspaces of tensor product of full Fock spaces and noncommutative varieties. We also obtain, in particular, by using techniques of noncommutative varieties, a classification of joint invariant subspaces of n-fold tensor products of Drury–Arveson spaces.

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Acknowledgements

We are deeply grateful to the referee for the valuable suggestions and comments. The research of the second named author is supported by NBHM post-doctoral fellowship no: 0204/27-/2019/R&D-II/12966. The third named author is supported in part by MATRICS (MTR/2017/000522), and CRG (CRG/2019/000908), by SERB (DST), and NBHM (NBHM/R.P.64/2014), Government of India.

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  1. Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, Bangalore, 560059, India

    Susmita Das, Deepak Kumar Pradhan & Jaydeb Sarkar

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  1. Susmita Das
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  2. Deepak Kumar Pradhan
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  3. Jaydeb Sarkar
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Correspondence to Jaydeb Sarkar.

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Das, S., Pradhan, D.K. & Sarkar, J. Submodules in Polydomains and Noncommutative Varieties. Integr. Equ. Oper. Theory 93, 23 (2021). https://doi.org/10.1007/s00020-021-02642-8

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  • DOI: https://doi.org/10.1007/s00020-021-02642-8

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