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Two Types of Invariant Subspaces in the Polydisc

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Abstract

It is known that the structure of invariant subspaces of the Hardy space \(H^{2}({{{\mathbb {D}}}}^n)\) on the polydisc \({{\mathbb {D}}}^n\) is very complicated; hence, we need good examples help us to understand the structure of invariant subspaces of \(H^2({{\mathbb {D}}}^n)\). In this paper, we define two types of invariant subspaces of \(H^2({{\mathbb {D}}}^n)\). Then, we give a characterization of these types invariant subspaces in view of the Beurling–Lax–Halmos Theorem. Unitary equivalence is also studied in this paper.

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  1. Department of Mathematics Science Faculty, Istanbul University, 34134, Istanbul, Turkey

    Beyaz Başak Koca

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  1. Beyaz Başak Koca
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Correspondence to Beyaz Başak Koca.

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Koca, B.B. Two Types of Invariant Subspaces in the Polydisc. Results Math 71, 1297–1305 (2017). https://doi.org/10.1007/s00025-016-0645-5

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  • DOI: https://doi.org/10.1007/s00025-016-0645-5

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