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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)].

MSC:

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

Citations:

Zbl 1155.47012
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References:

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[13] B. Yousefi and E. Hesameddini, Extension of the Beurling’s Theorem, Proc. Japan Acad. Ser. A Math. Sci. 84 (2008), no. 9, 167-169. · Zbl 1155.47012 · doi:10.3792/pjaa.84.167
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