Proceedings of the Japan Academy, Series A, Mathematical Sciences

Extension of the Beurling’s Theorem

Esmaiel Hesameddini and Bahmann Yousefi

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Abstract

Under some conditions on a Hilbert space $H$ of analytic functions on the open unit disc we will show that for every nontrivial invariant subspace $\mathcal{M}$ of $H$, there exists a unique nonconstant inner function $\varphi$ such that $\mathcal{M}=\varphi H$. This extends the Beurling’s Theorem.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 84, Number 9 (2008), 167-169.

Dates
First available in Project Euclid: 31 October 2008

Permanent link to this document
https://projecteuclid.org/euclid.pja/1225463780

Digital Object Identifier
doi:10.3792/pjaa.84.167

Mathematical Reviews number (MathSciNet)
MR2483601

Zentralblatt MATH identifier
1155.47012

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

Keywords
Invariant subspaces reproducing kernels inner functions multipliers

Citation

Yousefi, Bahmann; Hesameddini, Esmaiel. Extension of the Beurling’s Theorem. Proc. Japan Acad. Ser. A Math. Sci. 84 (2008), no. 9, 167--169. doi:10.3792/pjaa.84.167. https://projecteuclid.org/euclid.pja/1225463780


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