Doubly commuting mixed invariant subspaces in the polydisc
نویسندگان
چکیده
We obtain a complete characterization for doubly commuting mixed invariant subspaces of the Hardy space over unit polydisc. say closed subspace Q H2(Dn) is if Mzj(Q)⊆Q 1≤j≤k and Mzj⁎(Q)⊆Q, k+1≤j≤n some integer k∈{1,2,…,n−1}. prove that only ifQ=ΘH2(Dk)⊗Qθ1⊗⋯⊗Qθn−k, where Θ∈H∞(Dk) inner function Qθj either Jordan block H2(D)⊖θjH2(D) θj or H2(D). Furthermore, an explicit representation commutant n-tuple shifts as well tuple co-shifts are obtained. Finally, we discuss concrete examples subspaces.
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ژورنال
عنوان ژورنال: Bulletin Des Sciences Mathematiques
سال: 2021
ISSN: ['0007-4497', '1952-4773']
DOI: https://doi.org/10.1016/j.bulsci.2021.103051