Proceedings of the Japan Academy, Series A, Mathematical Sciences

Invariant subspaces of certain sub Hilbert spaces of $H^{2}$

Niteesh Sahni and Dinesh Singh

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Recently Yousefi and Hesameddini [13] have obtained a characterization for shift invariant subspaces of a special class of Hilbert spaces contained in the Hardy space $H^2$. In the present note we settle an open problem posed by them in their paper. In fact, by discussing invariance under multiplication by finite Blaschke factors we prove a far more general result than the main result of [13]. We prove our results under much weaker assumptions than the assumptions of [13] and with a simpler proof.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 4 (2011), 56-59.

First available in Project Euclid: 26 April 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Secondary: 47A25: Spectral sets

Invariant subspaces Blaschke factor inner function wold decomposition


Sahni, Niteesh; Singh, Dinesh. Invariant subspaces of certain sub Hilbert spaces of $H^{2}$. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 4, 56--59. doi:10.3792/pjaa.87.56.

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