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April 2011 Invariant subspaces of certain sub Hilbert spaces of $H^{2}$
Niteesh Sahni, Dinesh Singh
Proc. Japan Acad. Ser. A Math. Sci. 87(4): 56-59 (April 2011). DOI: 10.3792/pjaa.87.56

Abstract

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.

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Niteesh Sahni. Dinesh Singh. "Invariant subspaces of certain sub Hilbert spaces of $H^{2}$." Proc. Japan Acad. Ser. A Math. Sci. 87 (4) 56 - 59, April 2011. https://doi.org/10.3792/pjaa.87.56

Information

Published: April 2011
First available in Project Euclid: 26 April 2011

zbMATH: 1233.47027
MathSciNet: MR2803900
Digital Object Identifier: 10.3792/pjaa.87.56

Subjects:
Primary: 47B37
Secondary: 47A25

Keywords: Blaschke factor , inner function , invariant subspaces , Wold decomposition

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 4 • April 2011
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