Invariant subspaces of certain sub Hilbert spaces of \(H^{2}\). (English) Zbl 1233.47027

In the spirit of Beurling’s famous theorem on the invariant subspaces of the shift operator on \(H^2\), the authors give a description of certain subspaces \(H\) of \(H^2\) invariant under the multiplication operator \(T_B:H\to H\), \(f\mapsto Bf\), where \(B\) is a finite Blaschke product. Their theorem generalizes some results given in [B. Yousefi and E. Hesameddini [Proc. Japan. Acad., Ser. A 84, No. 9, 167–169 (2008; Zbl 1155.47012)].


47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A15 Invariant subspaces of linear operators
30J10 Blaschke products


Zbl 1155.47012
Full Text: DOI


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