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Generating Wandering Subspaces for Doubly Commuting Covariant Representations

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Abstract

We obtain a Halmos–Richter-type wandering subspace theorem for covariant representations of \(C^*\)-correspondences. Further the notion of Cauchy dual and a version of Shimorin’s Wold-type decomposition for covariant representations of \(C^*\)-correspondences is explored and as an application a wandering subspace theorem for doubly commuting covariant representations is derived. Using this wandering subspace theorem generating wandering subspaces are characterized for covariant representations of product systems in terms of the doubly commutativity condition.

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Acknowledgements

Shankar V. is grateful to The LNM Institute of Information Technology for providing research facility and warm hospitality during a visit in March 2019. Shankar V. is supported by CSIR Fellowship (File No: 09/115(0782)/2017-EMR-I).

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Authors and Affiliations

  1. The LNM Institute of Information Technology, Rupa ki Nangal, Post-Sumel, Via-Jamdoli, Jaipur, Rajasthan, 302031, India

    Harsh Trivedi

  2. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai (Madras), 600005, India

    Shankar Veerabathiran

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  1. Harsh Trivedi
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  2. Shankar Veerabathiran
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Correspondence to Harsh Trivedi.

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Trivedi, H., Veerabathiran, S. Generating Wandering Subspaces for Doubly Commuting Covariant Representations. Integr. Equ. Oper. Theory 91, 35 (2019). https://doi.org/10.1007/s00020-019-2533-3

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